Course Modules: Calculus with Infinitesimals

Course introduction

Course introduction Course introduction

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Course introduction Course introduction 1

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Why study calculus using infinitesimals? Why study calculus using infinitesimals? 2

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Algebra and trig skills review videos

Algebra and trig skills review videos Algebra and trig skills review videos

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real number line.mp4 real number line.mp4 1

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Attachment

inequalities.mp4 inequalities.mp4 2

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intervals.mp4 intervals.mp4 3

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absolute value.mp4 absolute value.mp4 4

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Attachment

absolute value equations and inequalities.mp4 absolute value equations and inequalities.mp4 5

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Attachment

distance on the number line.mp4 distance on the number line.mp4 6

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coordinate plane.mp4 coordinate plane.mp4 7

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Attachment

graph of an equation.mp4 graph of an equation.mp4 8

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Attachment

distance formula.mp4 distance formula.mp4 9

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Attachment

slopes of lines.mp4 slopes of lines.mp4 10

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Attachment

point-slope form of equation of line.mp4 point-slope form of equation of line.mp4 11

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Attachment

slope-intercept form of equation of line.mp4 slope-intercept form of equation of line.mp4 12

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parallel and perpendicular lines.mp4 parallel and perpendicular lines.mp4 13

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radians.mp4 radians.mp4 14

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Attachment

angles.mp4 angles.mp4 15

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Attachment

trig functions and rtheir values.mp4 trig functions and rtheir values.mp4 16

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Attachment

TI83 - TI84 trig functions (2:31) TI83 - TI84 trig functions (2:31) 17

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Attachment

finding additional trig values.mp4 finding additional trig values.mp4 18

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Attachment

useful trig identities.mp4 useful trig identities.mp4 19

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Attachment

basic trig graphs.mp4 basic trig graphs.mp4 20

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Functions review, part I: Section 0.4 lectures

Functions review, part I: Section 0.4 lectures Functions review, part I: Section 0.4 lectures

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Function representations Function representations 1

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Notes on graphical representations Notes on graphical representations 2

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Function values Function values 3

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Finding domains (and ranges) Finding domains (and ranges) 4

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Piecewise-defined functions Piecewise-defined functions 5

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Catalog of essential functions Catalog of essential functions 6

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External Url

(OPTIONAL) link to the Digital Library of Mathematical Functions (OPTIONAL) link to the Digital Library of Mathematical Functions 7

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Functions review, part II: Section 0.5 lectures

Functions review, part II: Section 0.5 lectures Functions review, part II: Section 0.5 lectures

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Shifting graphs Shifting graphs 1

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Reflections Reflections 2

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Stretching Stretching 3

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Combining functions Combining functions 4

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Composite functions Composite functions 5

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Infinitesimals: Section 1.1 lectures

Infinitesimals: Section 1.1 lectures Infinitesimals: Section 1.1 lectures

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It can't be done...or can it? It can't be done...or can it? 1

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Arithmetic with infinitesimals Arithmetic with infinitesimals 2

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Work lecture exercise 1 Work lecture exercise 1 3

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More levels of infinitesimals More levels of infinitesimals 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Infinite numbers Infinite numbers 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Two definitions Two definitions 8

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Transfer principle Transfer principle 9

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Work lecture exercise 4 Work lecture exercise 4 10

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Lecture exercises for infinitesimals Lecture exercises for infinitesimals 11

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The above file contains the lecture exercises. Each slide has an exercise followed by the answer. The lecture exercise file will always be at the end of the list of lectures. The above file contains the lecture exercises. Each slide has an exercise followed by the answer. The lecture exercise file will always be at the end of the list of lectures. 12

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Approximations: Section 1.2 lectures

Approximations: Section 1.2 lectures Approximations: Section 1.2 lectures

Attachment

Approximations Approximations 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Approximations: additional examples Approximations: additional examples 3

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Work lecture exercise 2 Work lecture exercise 2 4

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The Approximation Principle The Approximation Principle 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Approximations with fractions Approximations with fractions 7

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Work lecture exercise 4 Work lecture exercise 4 8

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(OPTIONAL) Two definitions (OPTIONAL) Two definitions 9

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Attachment

Absolute value approximations Absolute value approximations 10

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Lecture exercises for approximations Lecture exercises for approximations 11

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Hyperreals and functions: Section 1.3 lectures

Hyperreals and functions: Section 1.3 lectures Hyperreals and functions: Section 1.3 lectures

Attachment

Evaluating functions at hyperreals Evaluating functions at hyperreals 1

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Work lecture exercise 1 Work lecture exercise 1 2

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3 R's Principle 3 R's Principle 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Another twist: arbitrary infinitesimals Another twist: arbitrary infinitesimals 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Almost dividing by zero Almost dividing by zero 7

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Work lecture exercise 4 Work lecture exercise 4 8

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Evaluating a function at an infinite number Evaluating a function at an infinite number 9

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Work lecture exercise 5 Work lecture exercise 5 10

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Lecture exercises for hyperreals and functions Lecture exercises for hyperreals and functions 11

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Limits, part I: Section 1.4 lectures

Limits, part I: Section 1.4 lectures Limits, part I: Section 1.4 lectures

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Limits Limits 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Limits: holes in a graph Limits: holes in a graph 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Limit example with square root Limit example with square root 5

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Limit example with trig Limit example with trig 6

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Limit example with compound fraction Limit example with compound fraction 7

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Limit example with polynomial Limit example with polynomial 8

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Work lecture exercise 3 Work lecture exercise 3 9

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One-sided limits One-sided limits 10

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Work lecture exercise 4 Work lecture exercise 4 11

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Vertical asymptotes Vertical asymptotes 12

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Work lecture exercise 5 Work lecture exercise 5 13

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Lecture exercises for limits, part I Lecture exercises for limits, part I 14

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Limits, part II: Section 1.5 lectures

Limits, part II: Section 1.5 lectures Limits, part II: Section 1.5 lectures

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Limit examples with piecewise-defined functions Limit examples with piecewise-defined functions 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Finding limits graphically Finding limits graphically 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Sketching limits Sketching limits 5

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Numerical estimation of limits Numerical estimation of limits 6

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Limitations of graphically determining limits Limitations of graphically determining limits 7

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Screwy graphs: Mathematica file used in video Screwy graphs: Mathematica file used in video 8

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The Squeeze Theorem The Squeeze Theorem 9

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Work lecture exercise 3 Work lecture exercise 3 10

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Lecture exercises for limits, part II Lecture exercises for limits, part II 11

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Continuity, part I: Section 1.6 lectures

Continuity, part I: Section 1.6 lectures Continuity, part I: Section 1.6 lectures

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Continuity Continuity 1

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Verifying continuity Verifying continuity 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Identifying discontinuities graphically Identifying discontinuities graphically 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Identifying discontinuities algebraically Identifying discontinuities algebraically 6

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Work lecture exercise 3 Work lecture exercise 3 7

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An oscillatory discontinuity An oscillatory discontinuity 8

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Lecture exercises for continuity, part I Lecture exercises for continuity, part I 9

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Continuity, part II: Section 1.7 lectures

Continuity, part II: Section 1.7 lectures Continuity, part II: Section 1.7 lectures

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Continuous everywhere Continuous everywhere 1

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Using continuity to evaluate limits Using continuity to evaluate limits 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Combining continuous functions Combining continuous functions 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Intermediate Value Theorem Intermediate Value Theorem 6

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Application of IVT to root-finding Application of IVT to root-finding 7

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Work lecture exercise 3 Work lecture exercise 3 8

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(OPTIONAL) Linear functions are continuous (OPTIONAL) Linear functions are continuous 9

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(OPTIONAL) Polynomial functions are continuous (OPTIONAL) Polynomial functions are continuous 10

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(OPTIONAL) Proof of continuity for sin and cos (OPTIONAL) Proof of continuity for sin and cos 11

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(OPTIONAL) Proof of continuity for combinations of continuous functions (OPTIONAL) Proof of continuity for combinations of continuous functions 12

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(OPTIONAL) Proof of continuity for compositions of continuous functions (OPTIONAL) Proof of continuity for compositions of continuous functions 13

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Lecture exercises for continuity, part II Lecture exercises for continuity, part II 14

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Slopes and velocities: Section 1.8 lectures

Slopes and velocities: Section 1.8 lectures Slopes and velocities: Section 1.8 lectures

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Tangent lines, part 1 Tangent lines, part 1 1

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Tangent lines, part 2 Tangent lines, part 2 2

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Slope of tangent line: example for parabola Slope of tangent line: example for parabola 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 1 Work lecture exercise 1 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Slope of tangent line: example for rational function Slope of tangent line: example for rational function 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Slope of tangent line: example for square root Slope of tangent line: example for square root 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Average velocity Average velocity 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Average velocity example Average velocity example 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

Work lecture exercise 2 Work lecture exercise 2 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Instantaneous velocity Instantaneous velocity 10

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 3 Work lecture exercise 3 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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(OPTIONAL) Rates of change (OPTIONAL) Rates of change 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Lecture exercises for slopes and velocities Lecture exercises for slopes and velocities 13

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Limit review sheet answer videos

Limit review sheet answer videos Limit review sheet answer videos

Attachment

Limit review worksheet (Answers are in individual videos below; printable versions are in the next module) Limit review worksheet (Answers are in individual videos below; printable versions are in the next module) 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR1.mp4 LR1.mp4 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR2.mp4 LR2.mp4 3

attachment 417519 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR3.mp4 LR3.mp4 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR4.mp4 LR4.mp4 5

attachment 417521 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR5.mp4 LR5.mp4 6

attachment 417522 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR6.mp4 LR6.mp4 7

attachment 417523 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR7.mp4 LR7.mp4 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR8.mp4 LR8.mp4 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR9.mp4 LR9.mp4 10

attachment 417526 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR10.mp4 LR10.mp4 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR11.mp4 LR11.mp4 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR12.mp4 LR12.mp4 13

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR13.mp4 LR13.mp4 14

attachment 417530 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR14.mp4 LR14.mp4 15

attachment 417531 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR15.mp4 LR15.mp4 16

attachment 417532 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR16.mp4 LR16.mp4 17

attachment 417533 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR17.mp4 LR17.mp4 18

attachment 417534 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR18.mp4 LR18.mp4 19

attachment 417535 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR19.mp4 LR19.mp4 20

attachment 417536 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR20.mp4 LR20.mp4 21

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Limit review sheet answers: PDF (printable)

Limit review sheet answers: PDF (printable) Limit review sheet answers: PDF (printable)

Page

Each pencast below is an answer to a limit review worksheet exercise. Exercise 1 is explained in LR 1, exercise 2 in LR 2, etc. Each pencast below is an answer to a limit review worksheet exercise. Exercise 1 is explained in LR 1, exercise 2 in LR 2, etc. 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR 1 LR 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR 2 LR 2 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 3 LR 3 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 4 LR 4 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 5 LR 5 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR 6 LR 6 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 7 LR 7 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 8 LR 8 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 9 LR 9 10

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 10 LR 10 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 11 LR 11 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 12 LR 12 13

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 13 LR 13 14

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 14 LR 14 15

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR 15 LR 15 16

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

LR 16 LR 16 17

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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LR 17 LR 17 18

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Attachment

LR 18 LR 18 19

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Attachment

LR 19 LR 19 20

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Attachment

LR 20 LR 20 21

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

The derivative: Section 2.1 lectures

The derivative: Section 2.1 lectures The derivative: Section 2.1 lectures

Attachment

The derivative The derivative 1

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Page

Work lecture exercise 1 Work lecture exercise 1 2

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The derivative as a function The derivative as a function 3

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Page

Work lecture exercise 2 Work lecture exercise 2 4

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Attachment

Function graphs and derivatives: differentiability implies continuity Function graphs and derivatives: differentiability implies continuity 5

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Attachment

Function graphs and derivatives: corners Function graphs and derivatives: corners 6

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Function graphs and derivatives: vertical tangents Function graphs and derivatives: vertical tangents 7

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Page

Work lecture exercise 3 Work lecture exercise 3 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Notations for the derivative Notations for the derivative 9

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Local Linearity Theorem Local Linearity Theorem 10

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Lecture exercises for the derivative Lecture exercises for the derivative 11

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Derivative rules: Section 2.2 lectures

Derivative rules: Section 2.2 lectures Derivative rules: Section 2.2 lectures

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Derivative of a constant function Derivative of a constant function 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Derivatives of linear functions Derivatives of linear functions 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Power rule (version 1) Power rule (version 1) 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Constant multiple rule Constant multiple rule 7

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Work lecture exercise 4 Work lecture exercise 4 8

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Sum rule Sum rule 9

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Derivatives of polynomials Derivatives of polynomials 10

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Work lecture exercise 5 Work lecture exercise 5 11

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Higher-order derivatives Higher-order derivatives 12

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Work lecture exercise 6 Work lecture exercise 6 13

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Product rule Product rule 14

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Work lecture exercise 7 Work lecture exercise 7 15

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(OPTIONAL) Proof of product rule (OPTIONAL) Proof of product rule 16

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Quotient rule Quotient rule 17

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Work lecture exercise 8 Work lecture exercise 8 18

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(OPTIONAL) Proof of quotient rule (OPTIONAL) Proof of quotient rule 19

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Power rule for negative integers Power rule for negative integers 20

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Work lecture exercise 9 Work lecture exercise 9 21

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General power rule General power rule 22

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Lecture exercises for derivative rules Lecture exercises for derivative rules 23

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Tangent lines revisited: Section 2.3 lectures

Tangent lines revisited: Section 2.3 lectures Tangent lines revisited: Section 2.3 lectures

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Equations of tangent lines revisited Equations of tangent lines revisited 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Detecting horizontal tangent lines Detecting horizontal tangent lines 3

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Work lecture exercise 2 Work lecture exercise 2 4

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The graph of a function vs. the graph of its derivative The graph of a function vs. the graph of its derivative 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Local linearity Local linearity 7

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Mathematica file used in "Local linearity" video Mathematica file used in "Local linearity" video 8

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Local linearity, real and infinitesimal scales Local linearity, real and infinitesimal scales 9

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Linearizations Linearizations 10

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Work lecture exercise 4 Work lecture exercise 4 11

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Differentials Differentials 12

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Work lecture exercise 5 Work lecture exercise 5 13

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Lecture exercises for tangent lines revisited Lecture exercises for tangent lines revisited 14

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Trig derivatives: Section 2.4 lectures

Trig derivatives: Section 2.4 lectures Trig derivatives: Section 2.4 lectures

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(OPTIONAL) Proofs of two trig limits (OPTIONAL) Proofs of two trig limits 1

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Calculating trig limits Calculating trig limits 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Derivatives of sin and cos Derivatives of sin and cos 4

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Derivatives of the other four trig functions Derivatives of the other four trig functions 5

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Derivative examples with trig functions Derivative examples with trig functions 6

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Work lecture exercise 2 Work lecture exercise 2 7

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Why know derivatives of trig functions? Why know derivatives of trig functions? 8

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Lecture exercises for trig derivatives Lecture exercises for trig derivatives 9

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Chain rule: Section 2.5 lectures

Chain rule: Section 2.5 lectures Chain rule: Section 2.5 lectures

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Chain rule Chain rule 1

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Applying the chain rule: trig functions Applying the chain rule: trig functions 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Applying the chain rule: algebraic functions Applying the chain rule: algebraic functions 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Chain rule with product rule Chain rule with product rule 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Multiple-link chains Multiple-link chains 8

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Work lecture exercise 4 Work lecture exercise 4 9

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(OPTIONAL) Why radians instead of degrees? (OPTIONAL) Why radians instead of degrees? 10

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Lecture exercises for chain rule Lecture exercises for chain rule 11

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Implicit Differentiation: Section 2.6 lectures

Implicit Differentiation: Section 2.6 lectures Implicit Differentiation: Section 2.6 lectures

Attachment

Implicit differentiation Implicit differentiation 1

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(OPTIONAL) Making implicit explicit (OPTIONAL) Making implicit explicit 2

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Implicit differentiation example Implicit differentiation example 3

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Page

Work lecture exercise 1 Work lecture exercise 1 4

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Implicit differentiation example with product Implicit differentiation example with product 5

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Page

Work lecture exercise 2 Work lecture exercise 2 6

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(OPTIONAL) Implicit differentiation: another example (OPTIONAL) Implicit differentiation: another example 7

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Implicit differentiation: finding y'' Implicit differentiation: finding y'' 8

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Page

Work lecture exercise 3 Work lecture exercise 3 9

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(OPTIONAL) Proof of power rule for rational exponents (OPTIONAL) Proof of power rule for rational exponents 10

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Lecture exercises for implicit differentiation Lecture exercises for implicit differentiation 11

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Rates of change: Section 2.7 lectures

Rates of change: Section 2.7 lectures Rates of change: Section 2.7 lectures

Attachment

Motion Motion 1

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Attachment

Motion, example 1 Motion, example 1 2

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Page

Work lecture exercise 1 Work lecture exercise 1 3

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Attachment

Motion, example 2 Motion, example 2 4

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Attachment

Rates of change in economics Rates of change in economics 5

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Page

Work lecture exercise 2 Work lecture exercise 2 6

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Lecture exercises for rates of change Lecture exercises for rates of change 7

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Related rates, Pythagorean relationships: Section 2.8 lectures

Related rates, Pythagorean relationships: Section 2.8 lectures Related rates, Pythagorean relationships: Section 2.8 lectures

Attachment

Related rates: sliding ladder Related rates: sliding ladder 1

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Page

Work lecture exercise 1 Work lecture exercise 1 2

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Related rates: passing ships Related rates: passing ships 3

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Lecture exercise for related rates Lecture exercise for related rates 4

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(OPTIONAL) Related rates, Pythagorean relationships: additional worked examples

(OPTIONAL) Related rates, Pythagorean relationships: additional worked examples (OPTIONAL) Related rates, Pythagorean relationships: additional worked examples

Attachment

related rates_receding model airplane.mp4 related rates_receding model airplane.mp4 1

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Related rates: receding model airplane PDF Related rates: receding model airplane PDF 2

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related rates_approaching trains.mp4 related rates_approaching trains.mp4 3

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Related rates: approaching trains PDF Related rates: approaching trains PDF 4

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related rates_running the bases.mp4 related rates_running the bases.mp4 5

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Related rates: running the bases PDF Related rates: running the bases PDF 6

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related rates_stalking bobcat.mp4 related rates_stalking bobcat.mp4 7

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Related rates: stalking bobcat PDF Related rates: stalking bobcat PDF 8

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Related rates, non-Pythagorean relationships: Section 2.9 lectures

Related rates, non-Pythagorean relationships: Section 2.9 lectures Related rates, non-Pythagorean relationships: Section 2.9 lectures

Attachment

Related rates: streetlight shadow Related rates: streetlight shadow 1

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(OPTIONAL) Related rates, non-Pythagorean relationships: additional worked examples

(OPTIONAL) Related rates, non-Pythagorean relationships: additional worked examples (OPTIONAL) Related rates, non-Pythagorean relationships: additional worked examples

Attachment

related rates_deflating sphere.mp4 related rates_deflating sphere.mp4 1

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Related rates: deflating sphere PDF Related rates: deflating sphere PDF 2

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Attachment

related rates_rising water, example 2.mp4 related rates_rising water, example 2.mp4 3

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Related rates: rising water, example 2 PDF Related rates: rising water, example 2 PDF 4

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related rates_gravel pile.mp4 related rates_gravel pile.mp4 5

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Related rates: gravel pile PDF Related rates: gravel pile PDF 6

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related rates_changing angle.mp4 related rates_changing angle.mp4 7

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Related rates: changing angle PDF Related rates: changing angle PDF 8

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related rates_lengthening shadow.mp4 related rates_lengthening shadow.mp4 9

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Related rates: lengthening shadow PDF Related rates: lengthening shadow PDF 10

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Derivative review sheet answer videos

Derivative review sheet answer videos Derivative review sheet answer videos

Attachment

Derivative review worksheet (Answers are in individual videos below; printable versions are in the next module) Derivative review worksheet (Answers are in individual videos below; printable versions are in the next module) 1

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Page

Each video below answers a derivative review worksheet exercise. Exercise 1 is explained in DR 1, exercise 2 in DR 2, etc. Each video below answers a derivative review worksheet exercise. Exercise 1 is explained in DR 1, exercise 2 in DR 2, etc. 2

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DR 1.mp4 DR 1.mp4 3

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DR 2.mp4 DR 2.mp4 4

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DR 3.mp4 DR 3.mp4 5

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DR 4.mp4 DR 4.mp4 6

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DR 5.mp4 DR 5.mp4 7

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DR 6.mp4 DR 6.mp4 8

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DR 7.mp4 DR 7.mp4 9

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DR 8.mp4 DR 8.mp4 10

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Attachment

DR 9.mp4 DR 9.mp4 11

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DR 10.mp4 DR 10.mp4 12

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Attachment

DR 11.mp4 DR 11.mp4 13

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Attachment

DR 12.mp4 DR 12.mp4 14

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Attachment

DR 13.mp4 DR 13.mp4 15

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Attachment

DR 14.mp4 DR 14.mp4 16

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 15.mp4 DR 15.mp4 17

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 16.mp4 DR 16.mp4 18

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 17.mp4 DR 17.mp4 19

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 18.mp4 DR 18.mp4 20

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 19.mp4 DR 19.mp4 21

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 20.mp4 DR 20.mp4 22

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 21.mp4 DR 21.mp4 23

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Derivative review sheet answers: PDF (printable)

Derivative review sheet answers: PDF (printable) Derivative review sheet answers: PDF (printable)

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DR 1 DR 1 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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DR 2 DR 2 4

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DR 3 DR 3 5

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DR 4 DR 4 6

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DR 5 DR 5 7

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DR 6 DR 6 8

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DR 7 DR 7 9

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DR 8 DR 8 10

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DR 9 DR 9 11

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DR 10 DR 10 12

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DR 11 DR 11 13

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DR 12 DR 12 14

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DR 13 DR 13 15

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DR 14 DR 14 16

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DR 15 DR 15 17

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DR 16 DR 16 18

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DR 17 DR 17 19

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DR 18 DR 18 20

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DR 19 DR 19 21

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DR 20 DR 20 22

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DR 21 DR 21 23

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Absolute extrema: Section 3.1 lectures

Absolute extrema: Section 3.1 lectures Absolute extrema: Section 3.1 lectures

Attachment

Maximum and minimum values Maximum and minimum values 1

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Page

Work lecture exercise 1 Work lecture exercise 1 2

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Extreme Value Theorem Extreme Value Theorem 3

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Absolute extrema at endpoints Absolute extrema at endpoints 4

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Critical points Critical points 5

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Absolute extrema: continuous on [a,b] Absolute extrema: continuous on [a,b] 6

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Absolute extrema, example 2 Absolute extrema, example 2 7

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Page

Work lecture exercise 2 Work lecture exercise 2 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Absolute extrema, example 3 Absolute extrema, example 3 9

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(OPTIONAL) Proof of Fermat's theorem (OPTIONAL) Proof of Fermat's theorem 10

attachment 417703 0

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Lecture exercises for absolute extrema Lecture exercises for absolute extrema 11

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Mean Value Theorem: Section 3.2 lectures

Mean Value Theorem: Section 3.2 lectures Mean Value Theorem: Section 3.2 lectures

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Rolle's Theorem Rolle's Theorem 1

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Page

Work lecture exercise 1 Work lecture exercise 1 2

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Attachment

(OPTIONAL) An application of Rolle's Theorem (OPTIONAL) An application of Rolle's Theorem 3

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Attachment

Mean Value Theorem Mean Value Theorem 4

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Attachment

Mean Value Theorem example Mean Value Theorem example 5

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Page

Work lecture exercise 2 Work lecture exercise 2 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Functions with the same derivative Functions with the same derivative 7

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Page

Work lecture exercise 3 Work lecture exercise 3 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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(OPTIONAL) Proof of the Mean Value Theorem (OPTIONAL) Proof of the Mean Value Theorem 9

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Lecture exercises for Mean Value Theorem Lecture exercises for Mean Value Theorem 10

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Local extrema: Section 3.3 lectures

Local extrema: Section 3.3 lectures Local extrema: Section 3.3 lectures

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Increasing and decreasing functions Increasing and decreasing functions 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Finding intervals of increase or decrease Finding intervals of increase or decrease 3

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Page

Work lecture exercise 2 Work lecture exercise 2 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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First Derivative Test First Derivative Test 5

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Attachment

Finding local extrema, example 1 Finding local extrema, example 1 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Finding local extrema, example 2 Finding local extrema, example 2 8

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Work lecture exercise 4 Work lecture exercise 4 9

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Lecture exercises for local extrema Lecture exercises for local extrema 10

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Concavity: Section 3.4 lectures

Concavity: Section 3.4 lectures Concavity: Section 3.4 lectures

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Concavity Concavity 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Mathematica file used in "Concavity" video Mathematica file used in "Concavity" video 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Concavity and inflection points Concavity and inflection points 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Attachment

Determining concavity and inflection points, example 1 Determining concavity and inflection points, example 1 6

attachment 417729 0

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Work lecture exercise 3 Work lecture exercise 3 7

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Attachment

Determining concavity and inflection points, example 2 Determining concavity and inflection points, example 2 8

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Work lecture exercise 4 Work lecture exercise 4 9

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(OPTIONAL) Determining concavity and inflection points, example 3 (OPTIONAL) Determining concavity and inflection points, example 3 10

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Second Derivative Test Second Derivative Test 11

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Work lecture exercise 5 Work lecture exercise 5 12

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Lecture exercises for concavity Lecture exercises for concavity 13

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Curve sketching, polynomials: Section 3.5 lectures

Curve sketching, polynomials: Section 3.5 lectures Curve sketching, polynomials: Section 3.5 lectures

Attachment

Turning information into a sketch: polynomials Turning information into a sketch: polynomials 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Sketching polynomials, example 2 Sketching polynomials, example 2 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Polynomial sketch Polynomial sketch 5

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Avoiding concavity errors Avoiding concavity errors 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Lecture exercises for curve sketching, polynomials Lecture exercises for curve sketching, polynomials 8

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(OPTIONAL) Curve sketching, polynomials: additional worked example

(OPTIONAL) Curve sketching, polynomials: additional worked example (OPTIONAL) Curve sketching, polynomials: additional worked example

Attachment

curve sketching, polynomial, additional example.mp4 curve sketching, polynomial, additional example.mp4 1

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Curve sketching, polynomial, additional example PDF Curve sketching, polynomial, additional example PDF 2

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Limits at infinity: Section 3.6 lectures

Limits at infinity: Section 3.6 lectures Limits at infinity: Section 3.6 lectures

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Horizontal asymptotes and limits at infinity Horizontal asymptotes and limits at infinity 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Limits at infinity: examples Limits at infinity: examples 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Finding horizontal asymptotes Finding horizontal asymptotes 5

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Work lecture exercise 3 Work lecture exercise 3 6

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(OPTIONAL) Review: finding vertical asymptotes (OPTIONAL) Review: finding vertical asymptotes 7

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Limits at infinity: example with trig function Limits at infinity: example with trig function 8

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Lecture exercises for limits at infinity Lecture exercises for limits at infinity 9

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Curve sketching, general functions: Section 3.7 lectures

Curve sketching, general functions: Section 3.7 lectures Curve sketching, general functions: Section 3.7 lectures

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Turning information into a sketch: general functions Turning information into a sketch: general functions 1

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Curve sketching example: rational function Curve sketching example: rational function 2

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(OPTIONAL) Curve sketching (steps differ slightly from textbook due to being recorded before book was written) (OPTIONAL) Curve sketching (steps differ slightly from textbook due to being recorded before book was written) 3

attachment 417756 0

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(OPTIONAL) Curve sketching, general functions: additional worked example

(OPTIONAL) Curve sketching, general functions: additional worked example (OPTIONAL) Curve sketching, general functions: additional worked example

Attachment

curve sketching, rational function, additional example.mp4 curve sketching, rational function, additional example.mp4 1

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Curve sketching, rational function, additional example PDF Curve sketching, rational function, additional example PDF 2

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Optimization, part I: Section 3.8 lectures, part I

Optimization, part I: Section 3.8 lectures, part I Optimization, part I: Section 3.8 lectures, part I

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Optimization: example 1 Optimization: example 1 1

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(OPTIONAL) Optimization: volume of an open-top box (OPTIONAL) Optimization: volume of an open-top box 2

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(OPTIONAL) Optimization: best path (OPTIONAL) Optimization: best path 3

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(OPTIONAL) Optimization, part I: additional worked examples

(OPTIONAL) Optimization, part I: additional worked examples (OPTIONAL) Optimization, part I: additional worked examples

Attachment

optimization_volume of an open-top box, 2.mp4 optimization_volume of an open-top box, 2.mp4 1

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Optimization: volume of an open-top box, 2 PDF Optimization: volume of an open-top box, 2 PDF 2

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optimization_minimize fencing.mp4 optimization_minimize fencing.mp4 3

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Optimization: minimize fencing PDF Optimization: minimize fencing PDF 4

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Attachment

optimization_best path, 2.mp4 (NOTE: at the very end, 10 - x should be 10 - 0.629 = 9.371.) optimization_best path, 2.mp4 (NOTE: at the very end, 10 - x should be 10 - 0.629 = 9.371.) 5

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Optimization: best path, 2 PDF Optimization: best path, 2 PDF 6

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optimization_maximum sustainable yield.mp4 optimization_maximum sustainable yield.mp4 7

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Optimization: maximum sustainable yield PDF Optimization: maximum sustainable yield PDF 8

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Optimization, part II: Section 3.8 lectures, part II

Optimization, part II: Section 3.8 lectures, part II Optimization, part II: Section 3.8 lectures, part II

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Optimization: economics example Optimization: economics example 1

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Optimization: material in a can Optimization: material in a can 2

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(OPTIONAL) Optimization, part II: additional worked examples

(OPTIONAL) Optimization, part II: additional worked examples (OPTIONAL) Optimization, part II: additional worked examples

Attachment

optimization_material in a can, 2.mp4 optimization_material in a can, 2.mp4 1

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Optimization: material in a can, 2 PDF Optimization: material in a can, 2 PDF 2

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optimization_maximum profit.mp4 optimization_maximum profit.mp4 3

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Optimization: maximum profit PDF Optimization: maximum profit PDF 4

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optimization_maximum profit, 2.mp4 optimization_maximum profit, 2.mp4 5

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Optimization: maximum profit, 2 PDF Optimization: maximum profit, 2 PDF 6

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optimization_square in a circle.mp4 optimization_square in a circle.mp4 7

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Optimization: square in a circle PDF Optimization: square in a circle PDF 8

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Newton's method: Section 3.9 lectures

Newton's method: Section 3.9 lectures Newton's method: Section 3.9 lectures

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Newton's method Newton's method 1

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Newton's method example Newton's method example 2

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Work lecture exercise 1 Work lecture exercise 1 3

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TI-83/TI-84 shortcut for Newton's method TI-83/TI-84 shortcut for Newton's method 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Notes on Newton's method Notes on Newton's method 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Lecture exercises for Newton's method Lecture exercises for Newton's method 8

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Antiderivatives: Section 4.1 lectures

Antiderivatives: Section 4.1 lectures Antiderivatives: Section 4.1 lectures

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Antiderivatives Antiderivatives 1

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Indefinite integrals Indefinite integrals 2

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Antiderivative power rule Antiderivative power rule 3

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Work lecture exercise 1 Work lecture exercise 1 4

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Antiderivative constant multiple rule Antiderivative constant multiple rule 5

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Work lecture exercise 2 Work lecture exercise 2 6

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Antiderivative sum and difference rules Antiderivative sum and difference rules 7

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Work lecture exercise 3 Work lecture exercise 3 8

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Antiderivative of a constant Antiderivative of a constant 9

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Work lecture exercise 4 Work lecture exercise 4 10

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Manipulating integrands Manipulating integrands 11

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Trig antiderivatives Trig antiderivatives 12

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Work lecture exercise 5 Work lecture exercise 5 13

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Can we do it now? Can we do it now? 14

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Lecture exercises for antiderivatives Lecture exercises for antiderivatives 15

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Finite sums: Section 4.2 lectures

Finite sums: Section 4.2 lectures Finite sums: Section 4.2 lectures

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Estimating areas Estimating areas 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Midpoints Midpoints 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Upper and lower estimates Upper and lower estimates 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Lecture exercises for finite sums Lecture exercises for finite sums 7

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Areas and sums: Section 4.3 lectures

Areas and sums: Section 4.3 lectures Areas and sums: Section 4.3 lectures

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Summation notation Summation notation 1

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Work lecture exercise 1 Work lecture exercise 1 2

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Writing summation notation Writing summation notation 3

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Work lecture exercise 2 Work lecture exercise 2 4

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Helpful summation formulas Helpful summation formulas 5

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Work lecture exercise 3 Work lecture exercise 3 6

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Using summation formulas Using summation formulas 7

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Work lecture exercise 4 Work lecture exercise 4 8

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Areas revisited Areas revisited 9

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Area under y=x^3 on [0,2] Area under y=x^3 on [0,2] 10

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Work lecture exercise 5 Work lecture exercise 5 11

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Lecture exercises for areas and sums Lecture exercises for areas and sums 12

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Definite integral: Section 4.4 lectures

Definite integral: Section 4.4 lectures Definite integral: Section 4.4 lectures

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Definite integral Definite integral 1

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Using the definition of definite integral Using the definition of definite integral 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Notation Notation 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Net area Net area 6

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Properties of definite integrals Properties of definite integrals 7

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Using properties of integrals Using properties of integrals 8

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Work lecture exercise 3 Work lecture exercise 3 9

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Lecture exercises for definite integral Lecture exercises for definite integral 10

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Fundamental Theorem of Calculus: Section 4.5 lectures

Fundamental Theorem of Calculus: Section 4.5 lectures Fundamental Theorem of Calculus: Section 4.5 lectures

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Fundamental Theorem of Calculus, part I Fundamental Theorem of Calculus, part I 1

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Using FTC part I Using FTC part I 2

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Work lecture exercise 1 Work lecture exercise 1 3

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Fundamental Theorem of Calculus, part II Fundamental Theorem of Calculus, part II 4

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Using FTC part II Using FTC part II 5

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Work lecture exercise 2 Work lecture exercise 2 6

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More definite integral examples More definite integral examples 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 3 Work lecture exercise 3 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Lecture exercises for Fundamental Theorem of Calculus Lecture exercises for Fundamental Theorem of Calculus 9

attachment 417822 0

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Substitution for indefinite integrals: Section 4.6 lectures

Substitution for indefinite integrals: Section 4.6 lectures Substitution for indefinite integrals: Section 4.6 lectures

Attachment

Substitution Substitution 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 1 Work lecture exercise 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Substitution examples, part 1 Substitution examples, part 1 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 2 Work lecture exercise 2 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Substitution examples, part 2 Substitution examples, part 2 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Substitution examples, part 3 Substitution examples, part 3 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 3 Work lecture exercise 3 7

wiki_page 417829 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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When substitutions fail When substitutions fail 8

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Attachment

Lecture exercises for substitution for indefinite integrals Lecture exercises for substitution for indefinite integrals 9

attachment 417831 0

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Substitution for definite integrals: Section 4.7 lectures

Substitution for definite integrals: Section 4.7 lectures Substitution for definite integrals: Section 4.7 lectures

Attachment

Substitution with definite integrals Substitution with definite integrals 1

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Attachment

Definite integral substitution example Definite integral substitution example 2

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Page

Work lecture exercise 1 Work lecture exercise 1 3

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Attachment

Lecture exercise for substitution for definite integrals Lecture exercise for substitution for definite integrals 4

attachment 417835 0

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Numerical integration, part I: Section 4.8 lectures

Numerical integration, part I: Section 4.8 lectures Numerical integration, part I: Section 4.8 lectures

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Numerical integration introduction Numerical integration introduction 1

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Page

work lecture exercise 1 work lecture exercise 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Trapezoid rule Trapezoid rule 3

attachment 417906 0

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Attachment

Trapezoid rule example Trapezoid rule example 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 2 work lecture exercise 2 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Integration using the TI -83 or TI-84 calculators Integration using the TI -83 or TI-84 calculators 6

attachment 417909 0

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work lecture exercise 3 work lecture exercise 3 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Error estimate for the trapezoid rule Error estimate for the trapezoid rule 8

attachment 417911 0

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Attachment

Error estimate for the trapezoid rule, example 2 Error estimate for the trapezoid rule, example 2 9

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Attachment

Lecture exercises for numerical integration, part I Lecture exercises for numerical integration, part I 10

attachment 417913 0

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Numerical integration, part II: Section 4.9 lectures

Numerical integration, part II: Section 4.9 lectures Numerical integration, part II: Section 4.9 lectures

Attachment

Midpoint rule Midpoint rule 1

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Attachment

Simpson's rule Simpson's rule 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 1 work lecture exercise 1 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Derivation of formula for Simpson's rule (OPTIONAL) Derivation of formula for Simpson's rule (OPTIONAL) 4

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Error estimate for Simpson's rule (OPTIONAL) Error estimate for Simpson's rule (OPTIONAL) 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Comparing numerical integration methods Comparing numerical integration methods 6

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Lecture exercise for numerical integration, part II Lecture exercise for numerical integration, part II 7

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Initial value problems and net change: Section 4.10 lectures

Initial value problems and net change: Section 4.10 lectures Initial value problems and net change: Section 4.10 lectures

Attachment

Initial value problems (IVPs) Initial value problems (IVPs) 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Work lecture exercise 1 Work lecture exercise 1 2

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IVP: gravity IVP: gravity 3

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Net change Net change 4

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Work lecture exercise 2 Work lecture exercise 2 5

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Net change example Net change example 6

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Work lecture exercise 3 Work lecture exercise 3 7

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Lecture exercises for initial value problems and net change Lecture exercises for initial value problems and net change 8

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Integration skills review worksheet answer videos

Integration skills review worksheet answer videos Integration skills review worksheet answer videos

Attachment

Integration skills review worksheet (Answers are in individual videos below; printable versions are in the next module) Integration skills review worksheet (Answers are in individual videos below; printable versions are in the next module) 1

attachment 417382 0

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ISR 1.mp4 ISR 1.mp4 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 2.mp4 ISR 2.mp4 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 3.mp4 ISR 3.mp4 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 4.mp4 ISR 4.mp4 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 5.mp4 ISR 5.mp4 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 6.mp4 ISR 6.mp4 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 7.mp4 ISR 7.mp4 8

attachment 417850 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 7 alternate.mp4 ISR 7 alternate.mp4 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 8.mp4 ISR 8.mp4 10

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 9.mp4 ISR 9.mp4 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 10.mp4 ISR 10.mp4 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 11.mp4 ISR 11.mp4 13

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 12.mp4 ISR 12.mp4 14

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 13.mp4 ISR 13.mp4 15

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 14.mp4 ISR 14.mp4 16

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 15.mp4 ISR 15.mp4 17

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 16.mp4 ISR 16.mp4 18

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 16 alternate.mp4 ISR 16 alternate.mp4 19

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 17.mp4 ISR 17.mp4 20

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Integration skills review worksheet answers: PDF (printable)

Integration skills review worksheet answers: PDF (printable) Integration skills review worksheet answers: PDF (printable)

Page

Each pencast below is an answer to an integration skills review worksheet exercise. Exercise 1 is explained in ISR 1, exercise 2 in ISR 2, etc. Each pencast below is an answer to an integration skills review worksheet exercise. Exercise 1 is explained in ISR 1, exercise 2 in ISR 2, etc. 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 1 ISR 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 2 ISR 2 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 3 ISR 3 4

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 4 ISR 4 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 5 ISR 5 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 6 ISR 6 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 7 ISR 7 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 7 alternate ISR 7 alternate 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 8 ISR 8 10

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 9 ISR 9 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 10 ISR 10 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 11 ISR 11 13

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 12 ISR 12 14

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 13 ISR 13 15

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 14 ISR 14 16

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 15 ISR 15 17

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 16 ISR 16 18

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 16 alternate ISR 16 alternate 19

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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ISR 17 ISR 17 20

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Logarithms, part I: Section 5.1 lectures

Logarithms, part I: Section 5.1 lectures Logarithms, part I: Section 5.1 lectures

Attachment

The natural logarithmic function The natural logarithmic function 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 1 work lecture exercise 1 2

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Attachment

Getting familiar with y = ln x Getting familiar with y = ln x 3

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Page

work lecture exercise 2 work lecture exercise 2 4

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Attachment

Graph of y = ln x Graph of y = ln x 5

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Attachment

(OPTIONAL) Slow-rising graph (OPTIONAL) Slow-rising graph 6

attachment 417926 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Laws of logarithms Laws of logarithms 7

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Attachment

(OPTIONAL) Proof of third law of logarithms (OPTIONAL) Proof of third law of logarithms 8

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Attachment

Using the laws of logarithms Using the laws of logarithms 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 3 work lecture exercise 3 10

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Attachment

Differentiating logs, simplified Differentiating logs, simplified 11

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work lecture exercise 4 work lecture exercise 4 12

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Attachment

Asymptotes on y = ln x Asymptotes on y = ln x 13

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Attachment

Limits with logs Limits with logs 14

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Attachment

Lecture exercises for logarithms, part I Lecture exercises for logarithms, part I 15

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Logarithms, part II: Section 5.2 lectures

Logarithms, part II: Section 5.2 lectures Logarithms, part II: Section 5.2 lectures

Attachment

Domains of logarithmic functions Domains of logarithmic functions 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 1 work lecture exercise 1 2

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Attachment

Antiderivatives resulting in logarithms Antiderivatives resulting in logarithms 3

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Page

work lecture exercise 2 work lecture exercise 2 4

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Attachment

Integrals of tan and cot Integrals of tan and cot 5

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Page

work lecture exercise 3 work lecture exercise 3 6

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Attachment

Logarithmic differentiation Logarithmic differentiation 7

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Attachment

Lecture exercises for logarithms, part II Lecture exercises for logarithms, part II 8

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Inverse functions: Section 5.3 lectures

Inverse functions: Section 5.3 lectures Inverse functions: Section 5.3 lectures

Attachment

Inverse functions Inverse functions 1

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work lecture exercise 1 work lecture exercise 1 2

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Attachment

Finding inverses Finding inverses 3

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work lecture exercise 2 work lecture exercise 2 4

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Attachment

Graphs of inverse functions Graphs of inverse functions 5

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Page

work lecture exercise 3 work lecture exercise 3 6

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Attachment

Derivatives of inverse functions Derivatives of inverse functions 7

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Page

work lecture exercise 4 work lecture exercise 4 8

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Lecture exercises for inverse functions Lecture exercises for inverse functions 9

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Exponentials: Section 5.4 lectures

Exponentials: Section 5.4 lectures Exponentials: Section 5.4 lectures

Attachment

The natural exponential function The natural exponential function 1

attachment 417953 0

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Attachment

Calculus of natural exponentials Calculus of natural exponentials 2

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Attachment

Derivative and integral examples for natural exponentials Derivative and integral examples for natural exponentials 3

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work lecture exercises 1 and 2 work lecture exercises 1 and 2 4

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Laws of exponents Laws of exponents 5

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Review: algebra with logs and exponentials Review: algebra with logs and exponentials 6

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work lecture exercise 3 work lecture exercise 3 7

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Limits with exponentials Limits with exponentials 8

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Lecture exercises for exponentials Lecture exercises for exponentials 9

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finding compound limits graphically.mp4 finding compound limits graphically.mp4 10

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General exponentials: Section 5.5 lectures

General exponentials: Section 5.5 lectures General exponentials: Section 5.5 lectures

Attachment

General exponential functions General exponential functions 1

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(OPTIONAL) Laws of exponents for general exponentials (OPTIONAL) Laws of exponents for general exponentials 2

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Derivative and integral examples for general exponentials Derivative and integral examples for general exponentials 3

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work lecture exercise 1 work lecture exercise 1 4

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Comparing derivative rules Comparing derivative rules 5

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work lecture exercise 2 work lecture exercise 2 6

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(OPTIONAL) Power rule, general case (OPTIONAL) Power rule, general case 7

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Alternate definition of e Alternate definition of e 8

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Lecture exercises for general exponentials Lecture exercises for general exponentials 9

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General logarithms: Section 5.6 lectures

General logarithms: Section 5.6 lectures General logarithms: Section 5.6 lectures

Attachment

General logarithmic functions General logarithmic functions 1

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work lecture exercise 1 work lecture exercise 1 2

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(OPTIONAL) Laws of logarithms for general logarithms (OPTIONAL) Laws of logarithms for general logarithms 3

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Change of base property Change of base property 4

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work lecture exercise 2 work lecture exercise 2 5

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Calculus with general logarithmic functions Calculus with general logarithmic functions 6

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work lecture exercise 3 work lecture exercise 3 7

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Limits with general logarithms Limits with general logarithms 8

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Attachment

(OPTIONAL but fun!) Calculating exponentials by hand (OPTIONAL but fun!) Calculating exponentials by hand 9

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Attachment

Table of common logarithms (file from video) Table of common logarithms (file from video) 10

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Handwritten calculations for calculating exponentials by hand (file from video) Handwritten calculations for calculating exponentials by hand (file from video) 11

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Lecture exercises for general logarithms Lecture exercises for general logarithms 12

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Exponential growth and decay: Section 5.7 lectures

Exponential growth and decay: Section 5.7 lectures Exponential growth and decay: Section 5.7 lectures

Attachment

Exponential change Exponential change 1

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Exponential change, example 1 (growth) Exponential change, example 1 (growth) 2

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work lecture exercise 1 work lecture exercise 1 3

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(OPTIONAL) Exponential change, example 2 (decay) (OPTIONAL) Exponential change, example 2 (decay) 4

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Newton's Law of Cooling Newton's Law of Cooling 5

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(OPTIONAL) Derivation of formula for Newton's Law of Cooling (OPTIONAL) Derivation of formula for Newton's Law of Cooling 6

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Newton's Law of Cooling example Newton's Law of Cooling example 7

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work lecture exercise 2 work lecture exercise 2 8

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(OPTIONAL) Alternate derivation of continuously compounded interest formula (OPTIONAL) Alternate derivation of continuously compounded interest formula 9

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Lecture exercises for exponential growth and decay Lecture exercises for exponential growth and decay 10

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Inverse trig: Section 5.8 lectures

Inverse trig: Section 5.8 lectures Inverse trig: Section 5.8 lectures

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Inverse sine Inverse sine 1

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Derivative of inverse sine Derivative of inverse sine 2

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work lecture exercise 1 work lecture exercise 1 3

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Inverse cosine Inverse cosine 4

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Inverse tangent and cotangent Inverse tangent and cotangent 6

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work lecture exercise 3 work lecture exercise 3 7

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Inverse trig miscellaneous Inverse trig miscellaneous 8

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Integral formulas with inverse trig, part I Integral formulas with inverse trig, part I 9

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work lecture exercise 4 work lecture exercise 4 10

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Integral formulas with inverse trig, part II Integral formulas with inverse trig, part II 11

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Limits with inverse tangent Limits with inverse tangent 13

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(OPTIONAL) Review: cos(arctan(number)) (OPTIONAL) Review: cos(arctan(number)) 14

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Lecture exercises for inverse trig Lecture exercises for inverse trig 15

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Hyperbolic functions: Section 5.9 lectures

Hyperbolic functions: Section 5.9 lectures Hyperbolic functions: Section 5.9 lectures

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Hyperbolic functions Hyperbolic functions 1

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(OPTIONAL) Proof of cosh^2 t - sinh^2 t = 1 (OPTIONAL) Proof of cosh^2 t - sinh^2 t = 1 2

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Derivatives of hyperbolic functions Derivatives of hyperbolic functions 3

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work lecture exercise 1 work lecture exercise 1 4

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Inverse hyperbolic functions Inverse hyperbolic functions 5

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work lecture exercise 2 work lecture exercise 2 6

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Integrals with inverse hyperbolics Integrals with inverse hyperbolics 7

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work lecture exercise 3 work lecture exercise 3 8

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Derivative examples with hyperbolics Derivative examples with hyperbolics 9

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work lecture exercise 4 work lecture exercise 4 10

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Integral examples with hyperbolics Integral examples with hyperbolics 11

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work lecture exercise 5 work lecture exercise 5 12

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Hyperbolics on TI 83 - TI 84 Hyperbolics on TI 83 - TI 84 13

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work lecture exercise 6 work lecture exercise 6 14

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Lecture exercises for hyperbolic functions Lecture exercises for hyperbolic functions 15

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Comparing rates of growth: Section 5.10

Comparing rates of growth: Section 5.10 Comparing rates of growth: Section 5.10

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Faster growth means higher-level numbers Faster growth means higher-level numbers 1

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work lecture exercise 1 work lecture exercise 1 2

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Faster growth means eventually higher values Faster growth means eventually higher values 3

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Logarithmic growth rates Logarithmic growth rates 4

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(required for computer science students only) Computer science: big-oh notation (required for computer science students only) Computer science: big-oh notation 5

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Exponential growth rates Exponential growth rates 6

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work lecture exercise 2 work lecture exercise 2 7

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Lecture exercises for comparing rates of growth Lecture exercises for comparing rates of growth 8

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L'Hospital's Rule, part I: Section 5.11 lectures

L'Hospital's Rule, part I: Section 5.11 lectures L'Hospital's Rule, part I: Section 5.11 lectures

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Limits, indeterminate forms, and motivation Limits, indeterminate forms, and motivation 1

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L'Hospital's rule L'Hospital's rule 2

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L'Hospital's rule examples L'Hospital's rule examples 3

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work lecture exercise 1 work lecture exercise 1 4

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work lecture exercise 2 work lecture exercise 2 5

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L'Hospital's rule is for indeterminate forms only! L'Hospital's rule is for indeterminate forms only! 6

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(OPTIONAL) L'Hospital's rule and comparing levels of hyperreals (OPTIONAL) L'Hospital's rule and comparing levels of hyperreals 7

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Attachment

Lecture exercises for l'Hospital's Rule, part I Lecture exercises for l'Hospital's Rule, part I 8

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L'Hospital's Rule, part II: Section 5.12 lectures

L'Hospital's Rule, part II: Section 5.12 lectures L'Hospital's Rule, part II: Section 5.12 lectures

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Indeterminate form 0 times infinity Indeterminate form 0 times infinity 1

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work lecture exercise 1 work lecture exercise 1 2

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Indeterminate form infinity minus infinity Indeterminate form infinity minus infinity 3

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work lecture exercise 2 work lecture exercise 2 4

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Indeterminate forms 0^0, infinity^0, 1^infinity Indeterminate forms 0^0, infinity^0, 1^infinity 5

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work lecture exercise 3 work lecture exercise 3 6

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(OPTIONAL) Another alternate definition of e (OPTIONAL) Another alternate definition of e 7

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(OPTIONAL) Partial proof of l'Hospital's Rule (OPTIONAL) Partial proof of l'Hospital's Rule 8

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Lecture exercises for l'Hospital's Rule, part II Lecture exercises for l'Hospital's Rule, part II 9

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Section 5.13: note

Section 5.13: note Section 5.13: note

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Section 5.13 is optional. There are no recorded lectures for this section. Section 5.13 is optional. There are no recorded lectures for this section. 1

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Area between curves: Section 6.1 lectures

Area between curves: Section 6.1 lectures Area between curves: Section 6.1 lectures

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Area between curves Area between curves 1

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work lecture exercise 1 work lecture exercise 1 2

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Area enclosed by two curves Area enclosed by two curves 3

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work lecture exercise 2 work lecture exercise 2 4

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Area between curves: more complicated regions Area between curves: more complicated regions 5

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work lecture exercise 3 work lecture exercise 3 6

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Three curves Three curves 7

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Area between curves, sideways Area between curves, sideways 8

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Lecture exercises for area between curves Lecture exercises for area between curves 9

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Volumes part I: Section 6.2 lectures

Volumes part I: Section 6.2 lectures Volumes part I: Section 6.2 lectures

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Volume of a solid of revolution Volume of a solid of revolution 1

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Solid of revolution example: revolving about the x-axis Solid of revolution example: revolving about the x-axis 2

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work lecture exercise 1 work lecture exercise 1 3

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Rotating about the y-axis Rotating about the y-axis 4

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Solid of revolution example: revolving about the y-axis Solid of revolution example: revolving about the y-axis 5

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work lecture exercise 2 work lecture exercise 2 6

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Volumes by cross-sectional area Volumes by cross-sectional area 7

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(OPTIONAL) Volume of a wedge of wood, part I (OPTIONAL) Volume of a wedge of wood, part I 8

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Attachment

(OPTIONAL) Volume of a wedge of wood, part II (OPTIONAL) Volume of a wedge of wood, part II 9

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Lecture exercises for volumes, part I Lecture exercises for volumes, part I 10

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Volumes part II: Section 6.3 lectures

Volumes part II: Section 6.3 lectures Volumes part II: Section 6.3 lectures

Attachment

Solid of revolution example: revolving about y = -1 Solid of revolution example: revolving about y = -1 1

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Page

work lecture exercise 1 work lecture exercise 1 2

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Solid of revolution example: region between curves Solid of revolution example: region between curves 3

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work lecture exercise 2 work lecture exercise 2 4

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Lecture exercises for volumes, part II Lecture exercises for volumes, part II 5

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Shell method for volumes: Section 6.4 lectures

Shell method for volumes: Section 6.4 lectures Shell method for volumes: Section 6.4 lectures

Attachment

Subtracting volumes Subtracting volumes 1

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External Url

Shell method intro and example 1 Shell method intro and example 1 2

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External Url

Shell method example 2 Shell method example 2 3

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Page

work lecture exercise 1 work lecture exercise 1 4

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Attachment

Shell method example 3: horizontal axis of rotation Shell method example 3: horizontal axis of rotation 5

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work lecture exercise 2 work lecture exercise 2 6

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Attachment

Lecture exercises for shell method for volumes Lecture exercises for shell method for volumes 7

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Work, part I: Section 6.5 lectures

Work, part I: Section 6.5 lectures Work, part I: Section 6.5 lectures

Attachment

Work with constant force Work with constant force 1

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Page

work lecture exercise 1 work lecture exercise 1 2

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Attachment

Work with variable force Work with variable force 3

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Page

work lecture exercise 2 work lecture exercise 2 4

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Attachment

Work: springs Work: springs 5

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work lecture exercise 3 work lecture exercise 3 6

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Attachment

Springs, example 2 (OPTIONAL) Springs, example 2 (OPTIONAL) 7

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Attachment

Lecture exercises for work, part I Lecture exercises for work, part I 8

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Work, part II: Section 6.6 lecture

Work, part II: Section 6.6 lecture Work, part II: Section 6.6 lecture

Attachment

Work: pumping water Work: pumping water 1

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Average value of a function: Section 6.7 lectures

Average value of a function: Section 6.7 lectures Average value of a function: Section 6.7 lectures

Attachment

Average value of a function Average value of a function 1

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Page

work lecture exercise 1 work lecture exercise 1 2

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Attachment

Derivation of formula for average value (OPTIONAL) Derivation of formula for average value (OPTIONAL) 3

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Attachment

Mean Value Theorem for Integrals Mean Value Theorem for Integrals 4

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Page

work lecture exercise 2 work lecture exercise 2 5

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Attachment

Lecture exercises for average value of a function Lecture exercises for average value of a function 6

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Algebra for integration: Section 7.1 lectures

Algebra for integration: Section 7.1 lectures Algebra for integration: Section 7.1 lectures

Attachment

Review: long division of polynomials (can be skipped if you are confident that you remember how to do this) Review: long division of polynomials (can be skipped if you are confident that you remember how to do this) 1

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Attachment

Integration utilizing long division Integration utilizing long division 2

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Page

work lecture exercise 1 work lecture exercise 1 3

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Attachment

Integrating 1/(ax+b) Integrating 1/(ax+b) 4

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Page

work lecture exercise 2 work lecture exercise 2 5

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Attachment

Review: completing the square (can be skipped if you are confident that you remember how to do this) Review: completing the square (can be skipped if you are confident that you remember how to do this) 6

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Attachment

Integration utilizing completing the square Integration utilizing completing the square 7

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Page

work lecture exercise 3 work lecture exercise 3 8

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Lecture exercises for algebra for integration Lecture exercises for algebra for integration 9

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Integration by parts: Section 7.2 lectures

Integration by parts: Section 7.2 lectures Integration by parts: Section 7.2 lectures

Attachment

Integration by parts Integration by parts 1

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Attachment

Integration by parts, example 1 Integration by parts, example 1 2

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Page

work lecture exercise 1 work lecture exercise 1 3

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Attachment

Integration by parts, example 2 (polynomial times trig) Integration by parts, example 2 (polynomial times trig) 4

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work lecture exercise 2 work lecture exercise 2 5

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Tabular integration Tabular integration 6

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Attachment

Integration by parts, example 3 (exponential times trig) Integration by parts, example 3 (exponential times trig) 7

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Attachment

Integration by parts, example 4 (logs, inverse trig, inv hyp) Integration by parts, example 4 (logs, inverse trig, inv hyp) 8

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Integration by parts, example 5 (substitution and parts) Integration by parts, example 5 (substitution and parts) 9

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Integration by parts, definite integrals Integration by parts, definite integrals 10

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work lecture exercise 3 work lecture exercise 3 11

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Lecture exercises for parts Lecture exercises for parts 12

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Trig integrals: Section 7.3 lectures

Trig integrals: Section 7.3 lectures Trig integrals: Section 7.3 lectures

Attachment

Integral of secant Integral of secant 1

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work lecture exercise 1 work lecture exercise 1 2

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Attachment

Integral of cos^n x sin^m x dx, n or m odd Integral of cos^n x sin^m x dx, n or m odd 3

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work lecture exercise 2 work lecture exercise 2 4

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Attachment

Review: integral of sin kx dx (OPTIONAL) Review: integral of sin kx dx (OPTIONAL) 5

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Attachment

Integral of cos^n x sin^m x dx, n and m even Integral of cos^n x sin^m x dx, n and m even 6

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Attachment

Powers of tan x, sec x Powers of tan x, sec x 7

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Integral of sin mx cos nx dx Integral of sin mx cos nx dx 8

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work lecture exercise 3 work lecture exercise 3 9

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Lecture exercises for trig integrals Lecture exercises for trig integrals 10

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Trig substitution: Section 7.4 lectures

Trig substitution: Section 7.4 lectures Trig substitution: Section 7.4 lectures

Attachment

Trigonometric substitutions: motivating example Trigonometric substitutions: motivating example 1

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Attachment

Table of trigonometric substitutions Table of trigonometric substitutions 2

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work lecture exercise 1 work lecture exercise 1 3

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Multiple-technique example Multiple-technique example 4

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Lecture exercise for trig substitution Lecture exercise for trig substitution 5

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Partial fractions, part I: Section 7.5 lectures

Partial fractions, part I: Section 7.5 lectures Partial fractions, part I: Section 7.5 lectures

Attachment

Partial fractions Partial fractions 1

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work lecture exercise 1 work lecture exercise 1 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Partial fractions example Partial fractions example 3

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work lecture exercise 2 work lecture exercise 2 4

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Partial fractions example: improper fraction Partial fractions example: improper fraction 5

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work lecture exercise 3 work lecture exercise 3 6

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Attachment

Lecture exercises for partial fractions, part I Lecture exercises for partial fractions, part I 7

attachment 418157 0

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Partial fractions, part II: Section 7.6 lectures

Partial fractions, part II: Section 7.6 lectures Partial fractions, part II: Section 7.6 lectures

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Partial fraction forms Partial fraction forms 1

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work lecture exercise 1 work lecture exercise 1 2

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Attachment

Partial fractions example: repeated linear factor Partial fractions example: repeated linear factor 3

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work lecture exercise 2 work lecture exercise 2 4

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Partial fractions example: irreducible quadratic factor Partial fractions example: irreducible quadratic factor 5

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work lecture exercise 3 work lecture exercise 3 6

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Attachment

Lecture exercises for partial fractions, part II Lecture exercises for partial fractions, part II 7

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Sections 7.7-7.9: note

Sections 7.7-7.9: note Sections 7.7-7.9: note

Page

Section 7.7 is optional. There are no recorded lectures for sections 7.8 and 7.9. Section 7.8 is covered with the integral review worksheet; section 7.9 can be read in the textbook. Section 7.7 is optional. There are no recorded lectures for sections 7.8 and 7.9. Section 7.8 is covered with the integral review worksheet; section 7.9 can be read in the textbook. 1

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Type I improper integrals: Section 7.10 lectures

Type I improper integrals: Section 7.10 lectures Type I improper integrals: Section 7.10 lectures

Attachment

Improper integrals, type I: integrating to infinity Improper integrals, type I: integrating to infinity 1

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work lecture exercise 1 work lecture exercise 1 2

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Attachment

Type I improper integral example: from -infinity to infinity Type I improper integral example: from -infinity to infinity 3

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work lecture exercise 2 work lecture exercise 2 4

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Attachment

Why do integral from -infinity to infinity in two pieces? (OPTIONAL) Why do integral from -infinity to infinity in two pieces? (OPTIONAL) 5

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Divergent but not to infinity Divergent but not to infinity 6

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p-test for integrals p-test for integrals 7

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work lecture exercise 3 work lecture exercise 3 8

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Proof of p-test for integrals (OPTIONAL) Proof of p-test for integrals (OPTIONAL) 9

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Comparison theorem Comparison theorem 10

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Lecture exercises for type I improper integrals Lecture exercises for type I improper integrals 11

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Type II improper integrals: Section 7.11 lectures

Type II improper integrals: Section 7.11 lectures Type II improper integrals: Section 7.11 lectures

Attachment

Improper integrals, type II: handling discontinuities Improper integrals, type II: handling discontinuities 1

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Type II improper integral, example 1 Type II improper integral, example 1 2

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work lecture exercise 1 work lecture exercise 1 3

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Type II improper integral, example 2 Type II improper integral, example 2 4

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work lecture exercise 2 work lecture exercise 2 5

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Type II improper integrals: why? Type II improper integrals: why? 6

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work lecture exercise 3 work lecture exercise 3 7

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Lecture exercises for type II improper integrals Lecture exercises for type II improper integrals 8

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Integral Review Sheet answer videos

Integral Review Sheet answer videos Integral Review Sheet answer videos

Attachment

Integral review sheet (Answers are in individual videos below; printable versions are in the next module) Integral review sheet (Answers are in individual videos below; printable versions are in the next module) 1

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IR 1 IR 1 2

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IR 2 IR 2 3

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IR 3 easiest IR 3 easiest 4

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IR 3 alternate IR 3 alternate 5

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IR 4 IR 4 6

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IR 5 straightforward IR 5 straightforward 7

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IR 5 alternate (shorter) IR 5 alternate (shorter) 8

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IR 6 easiest IR 6 easiest 9

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IR 6 alternate IR 6 alternate 10

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IR 7 easiest IR 7 easiest 11

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IR 7 alternate IR 7 alternate 12

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IR 8 IR 8 13

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IR 8 substitution does not work IR 8 substitution does not work 14

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IR 9 IR 9 15

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IR 10 IR 10 16

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IR 11 IR 11 17

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IR 12 IR 12 18

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IR 13 usual method IR 13 usual method 19

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IR 13 tabular integration IR 13 tabular integration 20

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IR 14 option 1 IR 14 option 1 21

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IR 14 option 2 IR 14 option 2 22

attachment 418204 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 14 switching parts does not work IR 14 switching parts does not work 23

attachment 418205 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 15 easiest IR 15 easiest 24

attachment 418206 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 15 alternate IR 15 alternate 25

attachment 418207 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 16 IR 16 26

attachment 418208 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 17 IR 17 27

attachment 418209 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 18 option 1 IR 18 option 1 28

attachment 418210 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 18 option 2 IR 18 option 2 29

attachment 418211 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 19 IR 19 30

attachment 418212 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 20 correct IR 20 correct 31

attachment 418213 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 20 incorrect solution IR 20 incorrect solution 32

attachment 418214 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 21 IR 21 33

attachment 418215 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 22 usual IR 22 usual 34

attachment 418216 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 22 alternate IR 22 alternate 35

attachment 418217 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 23 easiest IR 23 easiest 36

attachment 418218 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 23 alternate IR 23 alternate 37

attachment 418219 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Integral Review Sheet answers: PDF (printable)

Integral Review Sheet answers: PDF (printable) Integral Review Sheet answers: PDF (printable)

Attachment

IR 1 IR 1 2

attachment 418221 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 2 IR 2 3

attachment 418222 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 3 easiest IR 3 easiest 4

attachment 418223 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 3 alternate IR 3 alternate 5

attachment 418224 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 4 IR 4 6

attachment 418225 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 5 straightforward IR 5 straightforward 7

attachment 418226 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 5 alternate (shorter) IR 5 alternate (shorter) 8

attachment 418227 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 6 easiest IR 6 easiest 9

attachment 418228 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 6 alternate IR 6 alternate 10

attachment 418229 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 7 easiest IR 7 easiest 11

attachment 418230 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 7 alternate IR 7 alternate 12

attachment 418231 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 8 IR 8 13

attachment 418232 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 8 substitution does not work IR 8 substitution does not work 14

attachment 418233 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 9 IR 9 15

attachment 418234 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 10 IR 10 16

attachment 418235 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 11 IR 11 17

attachment 418236 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 12 IR 12 18

attachment 418237 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 13 usual method IR 13 usual method 19

attachment 418238 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 13 tabular integration IR 13 tabular integration 20

attachment 418239 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 14 option 1 IR 14 option 1 21

attachment 418240 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 14 option 2 IR 14 option 2 22

attachment 418241 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 14 switching parts does not work IR 14 switching parts does not work 23

attachment 418242 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 15 easiest IR 15 easiest 24

attachment 418243 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 15 alternate IR 15 alternate 25

attachment 418244 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 16 IR 16 26

attachment 418245 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 17 IR 17 27

attachment 418246 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 18 option 1 IR 18 option 1 28

attachment 418247 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 18 option 2 IR 18 option 2 29

attachment 418248 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 19 IR 19 30

attachment 418249 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 20 correct solution (classical) IR 20 correct solution (classical) 31

attachment 418250 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 20 correct solution IR 20 correct solution 32

attachment 418251 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 20 incorrect solution IR 20 incorrect solution 33

attachment 418252 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 21 (classical) IR 21 (classical) 34

attachment 418253 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 21 IR 21 35

attachment 418254 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 22 usual method IR 22 usual method 36

attachment 418255 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 22 alternate solution IR 22 alternate solution 37

attachment 418256 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 23 easiest IR 23 easiest 38

attachment 418257 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

IR 23 alternate IR 23 alternate 39

attachment 418258 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete

Parametric equations: Section 8.1 lectures

Parametric equations: Section 8.1 lectures Parametric equations: Section 8.1 lectures

Attachment

Parametric equations Parametric equations 1

attachment 418097 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Parametric equations example Parametric equations example 2

attachment 418098 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 1 work lecture exercise 1 3

wiki_page 418099 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

TI 83/84: Parametric equations TI 83/84: Parametric equations 4

attachment 418100 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 2 work lecture exercise 2 5

wiki_page 418101 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Parameterization of a line segment Parameterization of a line segment 6

attachment 418102 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 3 work lecture exercise 3 7

wiki_page 418103 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Attachment

Parameterization of a circle Parameterization of a circle 8

attachment 418104 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Page

work lecture exercise 4 work lecture exercise 4 9

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(OPTIONAL) Families of curves (OPTIONAL) Families of curves 10

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Lecture exercises for parametric equations Lecture exercises for parametric equations 11

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Tangents to parametric curves: Section 8.2 lectures

Tangents to parametric curves: Section 8.2 lectures Tangents to parametric curves: Section 8.2 lectures

Attachment

Tangents to parameterized curves Tangents to parameterized curves 1

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work lecture exercise 1 work lecture exercise 1 2

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Example: tangents to parameterized curves Example: tangents to parameterized curves 3

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work lecture exercise 2 work lecture exercise 2 4

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Second derivatives with parameterized curves Second derivatives with parameterized curves 5

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work lecture exercise 3 work lecture exercise 3 6

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Lecture exercises for tangents to parametric curves Lecture exercises for tangents to parametric curves 7

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Polar coordinates: Section 8.3 lectures

Polar coordinates: Section 8.3 lectures Polar coordinates: Section 8.3 lectures

Attachment

Polar coordinates Polar coordinates 1

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work lecture exercise 1 work lecture exercise 1 2

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Polar equations and inequalities Polar equations and inequalities 3

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work lecture exercise 2 work lecture exercise 2 4

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Graphing polar curves Graphing polar curves 5

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Graphing colar curves, example 2 (OPTIONAL) Graphing colar curves, example 2 (OPTIONAL) 6

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TI 83 - TI 84 polar equations TI 83 - TI 84 polar equations 7

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work lecture exercise 3 work lecture exercise 3 8

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Lecture exercises for polar coordinates Lecture exercises for polar coordinates 9

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Tangents to polar curves: Section 8.4 lectures

Tangents to polar curves: Section 8.4 lectures Tangents to polar curves: Section 8.4 lectures

Attachment

Polar-rectangular conversions Polar-rectangular conversions 1

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work lecture exercise 1 work lecture exercise 1 2

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Tangents to polar curves Tangents to polar curves 3

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work lecture exercise 2 work lecture exercise 2 4

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Attachment

Tangents to polar curves, example 2 (OPTIONAL) Tangents to polar curves, example 2 (OPTIONAL) 5

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Polar circles Polar circles 6

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Lecture exercises for tangents to polar curves Lecture exercises for tangents to polar curves 7

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Conic sections: Section 8.5 lectures

Conic sections: Section 8.5 lectures Conic sections: Section 8.5 lectures

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Conic sections Conic sections 1

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Conic sections: circles Conic sections: circles 2

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Conic sections: parabolas Conic sections: parabolas 3

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work lecture exercise 1 work lecture exercise 1 4

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parabolas: examples parabolas: examples 5

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Conic sections: ellipses Conic sections: ellipses 6

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work lecture exercise 2 work lecture exercise 2 7

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Derivation of ellipse formula (OPTIONAL) Derivation of ellipse formula (OPTIONAL) 8

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work lecture exercise 3 work lecture exercise 3 9

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Ellipse example 1 Ellipse example 1 10

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Ellipse example 2 (OPTIONAL) Ellipse example 2 (OPTIONAL) 11

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Conic sections: hyperbolas Conic sections: hyperbolas 12

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Reflective properties of conics Reflective properties of conics 13

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Lecture exercises for conic sections Lecture exercises for conic sections 14

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Conic sections in polar coordinates: Section 8.6 lectures

Conic sections in polar coordinates: Section 8.6 lectures Conic sections in polar coordinates: Section 8.6 lectures

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Eccentricity Eccentricity 1

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work lecture exercise 1 work lecture exercise 1 2

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work lecture exercise 2 work lecture exercise 2 3

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Polar equation of a conic section, e > 0 Polar equation of a conic section, e > 0 4

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work lecture exercise 3 work lecture exercise 3 5

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Alternate polar form for ellipses Alternate polar form for ellipses 6

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work lecture exercise 4 work lecture exercise 4 7

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Earth's orbit Earth's orbit 8

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Polar form of a conic: example Polar form of a conic: example 9

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Lecture exercises for conic sections in polar coordinates Lecture exercises for conic sections in polar coordinates 10

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Arc length: Section 9.1 lectures

Arc length: Section 9.1 lectures Arc length: Section 9.1 lectures

Attachment

Arc length Arc length 1

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Arc length example 1 Arc length example 1 2

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work lecture exercise 1 work lecture exercise 1 3

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Arc length example 2 Arc length example 2 4

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work lecture exercise 2 work lecture exercise 2 5

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Lecture exercises for arc length Lecture exercises for arc length 6

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Areas and lengths in polar coordinates: Section 9.2 lectures

Areas and lengths in polar coordinates: Section 9.2 lectures Areas and lengths in polar coordinates: Section 9.2 lectures

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Areas in polar coordinates Areas in polar coordinates 1

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Polar area example Polar area example 2

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work lecture exercise 1 work lecture exercise 1 3

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Lengths in polar coordinates Lengths in polar coordinates 4

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Polar length example Polar length example 5

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work lecture exercise 2 work lecture exercise 2 6

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Intersections of polar curves (OPTIONAL) Intersections of polar curves (OPTIONAL) 7

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Lecture exercises for lengths and areas in polar coordinates Lecture exercises for lengths and areas in polar coordinates 8

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Surface area: Section 9.3 lectures

Surface area: Section 9.3 lectures Surface area: Section 9.3 lectures

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Area of a surface of revolution Area of a surface of revolution 1

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Surface area example 1 Surface area example 1 2

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work lecture exercise 1 work lecture exercise 1 3

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Surface area, rotating y=f(x) about y-axis Surface area, rotating y=f(x) about y-axis 4

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Surface area example 2 Surface area example 2 5

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work lecture exercise 2 work lecture exercise 2 6

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Lecture exercises for surface area Lecture exercises for surface area 7

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Lengths and surface areas with parametric curves: Section 9.4 lectures

Lengths and surface areas with parametric curves: Section 9.4 lectures Lengths and surface areas with parametric curves: Section 9.4 lectures

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Lengths of parameterized curves Lengths of parameterized curves 1

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Parametric arc length example Parametric arc length example 2

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work lecture exercise 1 work lecture exercise 1 3

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Surface areas using parametric curves Surface areas using parametric curves 4

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Parametric surface area example Parametric surface area example 5

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work lecture exercise 2 work lecture exercise 2 6

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Lecture exercises for lengths and surface areas with parametric curves Lecture exercises for lengths and surface areas with parametric curves 7

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Hydrostatic pressure and force: Section 9.5 lectures

Hydrostatic pressure and force: Section 9.5 lectures Hydrostatic pressure and force: Section 9.5 lectures

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Fluid pressure and force Fluid pressure and force 1

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work lecture exercise 1 work lecture exercise 1 2

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Fluid force example: vertical plate Fluid force example: vertical plate 3

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work lecture exercise 2 work lecture exercise 2 4

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Fluid force example 2 Fluid force example 2 5

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work lecture exercise 3 work lecture exercise 3 6

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Lecture exercises for hydrostatic pressure and force Lecture exercises for hydrostatic pressure and force 7

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Centers of mass: Section 9.6 lectures

Centers of mass: Section 9.6 lectures Centers of mass: Section 9.6 lectures

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Moments and centers of mass Moments and centers of mass 1

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Center of mass example Center of mass example 2

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Page

work lecture exercise 1 work lecture exercise 1 3

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Center of mass: thin flat plates of constant density Center of mass: thin flat plates of constant density 4

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Center of mass example (thin flat plate) Center of mass example (thin flat plate) 5

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work lecture exercise 2 work lecture exercise 2 6

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(OPTIONAL) Center of mass example 2 (thin flat plate) (OPTIONAL) Center of mass example 2 (thin flat plate) 7

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Lecture exercises for moments and centers of mass Lecture exercises for moments and centers of mass 8

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Applications to economics: Section 9.7 lectures

Applications to economics: Section 9.7 lectures Applications to economics: Section 9.7 lectures

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Consumers' surplus Consumers' surplus 1

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work lecture exercise 1 work lecture exercise 1 2

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Producers' surplus Producers' surplus 3

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Consumers' and producers' surplus simultaneously Consumers' and producers' surplus simultaneously 4

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Gini coefficient of income distribution Gini coefficient of income distribution 5

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work lecture exercise 2 work lecture exercise 2 6

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Numerical approximation to Gini coefficient Numerical approximation to Gini coefficient 7

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(OPTIONAL) Review: net change theorem (OPTIONAL) Review: net change theorem 8

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Lecture exercises for applications to economics Lecture exercises for applications to economics 9

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The logistic equation: Section 9.8 lectures

The logistic equation: Section 9.8 lectures The logistic equation: Section 9.8 lectures

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Restrained growth Restrained growth 1

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(OPTIONAL) Solving the logistic differential equation (OPTIONAL) Solving the logistic differential equation 2

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Example: the comparing exponential and logistic models Example: the comparing exponential and logistic models 3

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Logistic growth example: declining population Logistic growth example: declining population 4

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(OPTIONAL) Have you heard....? (OPTIONAL) Have you heard....? 5

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There are no lecture exercises for this section. There are no lecture exercises for this section. 6

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Chapter 10: note

Chapter 10: note Chapter 10: note

Page

Many chapter 10 lectures need modification and will be added at a later date. Many chapter 10 lectures need modification and will be added at a later date. 1

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