Course Modules

Week6 Lecture Notes

Week6 Lecture Notes Week6 Lecture Notes

Assignment

Final Exam Final Exam 30 1

assignment 2590742 1

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Assignment

Submission of Final Exam Submission of Final Exam 5 2

assignment 2592930 1

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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

Calculus2 Sec7.3[14022].pdf Calculus2 Sec7.3[14022].pdf 3

attachment 2591601 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 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

Calculus2 Sec7.1[14021].pdf Calculus2 Sec7.1[14021].pdf 4

attachment 2591602 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 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

Calculus2 Sec6.3 [13996].pdf Calculus2 Sec6.3 [13996].pdf 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 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

Imported Content

Imported Content Imported Content

Assignment

Final Exam Final Exam 30 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 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

Week5 Lecture Notes

Week5 Lecture Notes Week5 Lecture Notes

Assignment

Exam 2 Exam 2 50 1

assignment 2587080 1

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Assignment

Submission of Exam 2 Submission of Exam 2 5 2

assignment 2587081 1

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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

Calculus2 Sec6.2[13968].pdf Calculus2 Sec6.2[13968].pdf 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 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

Calculus2 Sec5.6[13921].pdf Calculus2 Sec5.6[13921].pdf 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 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

Calculus2 Sec5.5[13911].pdf Calculus2 Sec5.5[13911].pdf 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 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

Calculus2 Sec5.4 [13910].pdf Calculus2 Sec5.4 [13910].pdf 6

attachment 2584727 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 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

Calculus2 Sec6.1[13947].pdf Calculus2 Sec6.1[13947].pdf 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 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

Week4 Lecture Notes

Week4 Lecture Notes Week4 Lecture Notes

Attachment

Calculus2 Sec5.2[13871].pdf Calculus2 Sec5.2[13871].pdf 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 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

Calculus2 Sec5.1[13849].pdf Calculus2 Sec5.1[13849].pdf 2

attachment 2577949 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 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

Calculus2 Sec5.3[13886].pdf Calculus2 Sec5.3[13886].pdf 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 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

Week3 Lecture Notes

Week3 Lecture Notes Week3 Lecture Notes

Attachment

Calculus2 Sec2.9[13756].pdf Calculus2 Sec2.9[13756].pdf 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 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

Calculus2 Sec2.4[13739].pdf Calculus2 Sec2.4[13739].pdf 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 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

Calculus2_ Sec2.3[13716].pdf Calculus2_ Sec2.3[13716].pdf 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 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

Calc Exam Info[13715].pdf Calc Exam Info[13715].pdf 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 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

Week2 Lecture Notes

Week2 Lecture Notes Week2 Lecture Notes

Attachment

Calculus2 Sec2.1[13636].pdf Calculus2 Sec2.1[13636].pdf 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 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

Calculus2 Sec3.7[13593].pdf Calculus2 Sec3.7[13593].pdf 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 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

Calculus2 Sec3.4[13492].pdf Calculus2 Sec3.4[13492].pdf 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 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

Calculus2 Sec2.2[13668].pdf Calculus2 Sec2.2[13668].pdf 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 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

Week 1 Lecture Notes

Week 1 Lecture Notes Week 1 Lecture Notes

Attachment

Double,Half Angle Formulas[13446].pdf Double,Half Angle Formulas[13446].pdf 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 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

Math3B Sec3.3[13433].pdf Math3B Sec3.3[13433].pdf 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 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

Math3B Sec3.2[13358].pdf Math3B Sec3.2[13358].pdf 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 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

Math3B Sec3.1[13311].pdf Math3B Sec3.1[13311].pdf 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 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

Calc 2

Calc 2 Calc 2

Context Module Sub Header

1.1 Approximating Areas 1

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Page

LEARNING OBJECTIVES 1.1 Approximating Areas LEARNING OBJECTIVES 1.1 Approximating Areas 2

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External Url

READ 1.1 Approximating Areas READ 1.1 Approximating Areas 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 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

VIEW 1.1 Approximating Areas VIEW 1.1 Approximating Areas 4

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Page

Riemann Sum demonstration Riemann Sum demonstration 6

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Context Module Sub Header

1.2 The Definite Integral 7

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Page

LEARNING OBJECTIVES 1.2 The Definite Integral LEARNING OBJECTIVES 1.2 The Definite Integral 8

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External Url

READ 1.2 The Definite Integral READ 1.2 The Definite Integral 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 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

VIEW 1.2 The Definite Integral VIEW 1.2 The Definite Integral 10

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Context Module Sub Header

1.3 The Fundamental Theorem of Calculus 12

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Page

LEARNING OBJECTIVES 1.3 The Fundamental Theorem of Calculus LEARNING OBJECTIVES 1.3 The Fundamental Theorem of Calculus 13

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External Url

READ 1.3 The Fundamental Theorem of Calculus READ 1.3 The Fundamental Theorem of Calculus 14

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Page

VIEW 1.3 The Fundamental Theorem of Calculus VIEW 1.3 The Fundamental Theorem of Calculus 15

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Context Module Sub Header

1.4 Integration Formulas and the Net Change Theorem 17

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Page

LEARNING OBJECTIVES 1.4 Integration Formulas and the Net Change Theorem LEARNING OBJECTIVES 1.4 Integration Formulas and the Net Change Theorem 18

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External Url

READ 1.4 Integration Formulas and the Net Change Theorem READ 1.4 Integration Formulas and the Net Change Theorem 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 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

VIEW 1.4 Integration Formulas and the Net Change Theorem VIEW 1.4 Integration Formulas and the Net Change Theorem 20

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Context Module Sub Header

1.5 Substitution 22

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Page

LEARNING OBJECTIVES 1.5 Substitution LEARNING OBJECTIVES 1.5 Substitution 23

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READ 1.5 Substitution READ 1.5 Substitution 24

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VIEW 1.5 Substitution VIEW 1.5 Substitution 25

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EXERCISES 1.5 Substitution EXERCISES 1.5 Substitution 100 26

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1.6 Integrals Involving Exponential and Logarithmic Functions 28

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LEARNING OBJECTIVES 1.6 Integrals Involving Exponential and Logarithmic Functions LEARNING OBJECTIVES 1.6 Integrals Involving Exponential and Logarithmic Functions 29

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READ 1.6 Integrals Involving Exponential and Logarithmic Functions READ 1.6 Integrals Involving Exponential and Logarithmic Functions 30

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VIEW 1.6 Integrals Involving Exponential and Logarithmic Functions VIEW 1.6 Integrals Involving Exponential and Logarithmic Functions 31

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EXERCISES 1.6 Integrals Involving Exponential & Logarithmic Functions EXERCISES 1.6 Integrals Involving Exponential & Logarithmic Functions 100 32

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1.7 Integrals Resulting in Inverse Trigonometric Functions 33

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LEARNING OBJECTIVES 1.7 Integrals Resulting in Inverse Trigonometric Functions LEARNING OBJECTIVES 1.7 Integrals Resulting in Inverse Trigonometric Functions 34

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READ 1.7 Integrals Resulting in Inverse Trigonometric Functions READ 1.7 Integrals Resulting in Inverse Trigonometric Functions 35

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VIEW 1.7 Integrals Resulting in Inverse Trigonometric Functions VIEW 1.7 Integrals Resulting in Inverse Trigonometric Functions 36

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EXERCISES 1.7 Integrals Resulting in Inverse Trig Functions EXERCISES 1.7 Integrals Resulting in Inverse Trig Functions 100 37

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Chapter 2 Applications of Integration 38

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2.1 Areas Between Curves 39

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LEARNING OBJECTIVES 2.1 Areas Between Curves LEARNING OBJECTIVES 2.1 Areas Between Curves 40

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READ 2.1 Areas Between Curves READ 2.1 Areas Between Curves 41

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Section 2.1 Video Lessons - Areas Between Curves Section 2.1 Video Lessons - Areas Between Curves 42

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EXERCISES 2.1 Areas Between Curves EXERCISES 2.1 Areas Between Curves 100 43

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2.2 Determining Volumes by Slicing 44

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LEARNING OBJECTIVES 2.2 Determining Volumes by Slicing LEARNING OBJECTIVES 2.2 Determining Volumes by Slicing 45

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READ 2.2 Determining Volumes by Slicing READ 2.2 Determining Volumes by Slicing 46

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VIEW 2.2 Determining Volumes by Slicing VIEW 2.2 Determining Volumes by Slicing 47

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EXERCISES 2.2 Determining Volumes by Slicing EXERCISES 2.2 Determining Volumes by Slicing 100 48

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2.3 Volumes of Revolution: Cylindrical Shells 49

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LEARNING OBJECTIVES 2.3 Volumes of Revolution: Cylindrical Shells LEARNING OBJECTIVES 2.3 Volumes of Revolution: Cylindrical Shells 50

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READ 2.3 Volumes of Revolution: Cylindrical Shells READ 2.3 Volumes of Revolution: Cylindrical Shells 51

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VIEW 2.3 Volumes of Revolution: Cylindrical Shells VIEW 2.3 Volumes of Revolution: Cylindrical Shells 52

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EXERCISES 2.3 Volumes of Revolution: Cylindrical Shells EXERCISES 2.3 Volumes of Revolution: Cylindrical Shells 100 53

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2.4 Arc Length of a Curve and Surface Area 54

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LEARNING OBJECTIVES 2.4 Arc Length of a Curve and Surface Area LEARNING OBJECTIVES 2.4 Arc Length of a Curve and Surface Area 55

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READ 2.4 Arc Length of a Curve and Surface Area READ 2.4 Arc Length of a Curve and Surface Area 56

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VIEW 2.4 Arc Length of a Curve and Surface Area VIEW 2.4 Arc Length of a Curve and Surface Area 57

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EXERCISES 2.4. Arc Length of a Curve and Surface Area EXERCISES 2.4. Arc Length of a Curve and Surface Area 80 58

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2.5 Physical Applications 59

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LEARNING OBJECTIVES 2.5 Physical Applications LEARNING OBJECTIVES 2.5 Physical Applications 60

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READ 2.5 Physical Applications READ 2.5 Physical Applications 61

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VIEW 2.5 Physical Applications VIEW 2.5 Physical Applications 62

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2.6 Moments and Centers of Mass 64

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LEARNING OBJECTIVES 2.6 Moments and Centers of Mass LEARNING OBJECTIVES 2.6 Moments and Centers of Mass 65

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READ 2.6 Moments and Centers of Mass READ 2.6 Moments and Centers of Mass 66

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VIEW 2.6 Moments and Centers of Mass VIEW 2.6 Moments and Centers of Mass 67

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2.7 Integrals, Exponential Functions, and Logarithms 69

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LEARNING OBJECTIVES 2.7 Integrals, Exponential Functions, and Logarithms LEARNING OBJECTIVES 2.7 Integrals, Exponential Functions, and Logarithms 70

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READ 2.7 Integrals, Exponential Functions, and Logarithms READ 2.7 Integrals, Exponential Functions, and Logarithms 71

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VIEW 2.7 Integrals, Exponential Functions, and Logarithms VIEW 2.7 Integrals, Exponential Functions, and Logarithms 72

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2.8 Exponential Growth and Decay 74

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LEARNING OBJECTIVES 2.8 Exponential Growth and Decay LEARNING OBJECTIVES 2.8 Exponential Growth and Decay 75

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READ 2.8 Exponential Growth and Decay READ 2.8 Exponential Growth and Decay 76

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VIEW 2.8 Exponential Growth and Decay VIEW 2.8 Exponential Growth and Decay 77

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2.9 Calculus of the Hyperbolic Functions 79

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LEARNING OBJECTIVES 2.9 Calculus of the Hyperbolic Functions LEARNING OBJECTIVES 2.9 Calculus of the Hyperbolic Functions 80

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READ 2.9 Calculus of the Hyperbolic Functions READ 2.9 Calculus of the Hyperbolic Functions 81

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VIEW 2.9 Calculus of Hyperbolic Functions VIEW 2.9 Calculus of Hyperbolic Functions 82

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EXERCISES 2.9 Calculus of Hyperbolic Functions EXERCISES 2.9 Calculus of Hyperbolic Functions 100 83

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Chapter 3 Techniques of Integration 84

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3.1 Integration by Parts 85

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LEARNING OBJECTIVES 3.1: Integration by Parts LEARNING OBJECTIVES 3.1: Integration by Parts 86

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READ 3.1 Integration by Parts READ 3.1 Integration by Parts 87

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VIEW 3.1 Integration by Parts VIEW 3.1 Integration by Parts 88

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Assignment

EXERCISES 3.1 - Integration by Parts EXERCISES 3.1 - Integration by Parts 100 89

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3.2 Trigonometric Integrals 90

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LEARNING OBJECTIVES 3.2 Trigonometric Integrals LEARNING OBJECTIVES 3.2 Trigonometric Integrals 91

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READ 3.2 Trigonometric Integrals READ 3.2 Trigonometric Integrals 92

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VIEW 3.2 Trigonometric Integrals VIEW 3.2 Trigonometric Integrals 93

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Assignment

EXERCISES 3.2 - Trig Integrals EXERCISES 3.2 - Trig Integrals 100 94

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3.3 Trigonometric Substitution 95

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LEARNING OBJECTIVES 3.3 Trigonometric Substitution LEARNING OBJECTIVES 3.3 Trigonometric Substitution 96

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READ 3.3 Trigonometric Substitution READ 3.3 Trigonometric Substitution 97

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Section 3.3 - Video Lessons Section 3.3 - Video Lessons 98

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EXERCISES 3.3 - Trigonometric Substitution EXERCISES 3.3 - Trigonometric Substitution 100 99

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3.4 Partial Fractions 100

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LEARNING OBJECTIVES 3.4 Partial Fractions LEARNING OBJECTIVES 3.4 Partial Fractions 101

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READ 3.4 Partial Fractions READ 3.4 Partial Fractions 102

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VIEW 3.4 Partial Fractions VIEW 3.4 Partial Fractions 103

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EXERCISES 3.4 Partial Fractions EXERCISES 3.4 Partial Fractions 100 104

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3.6 Numerical Integration 105

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LEARNING OBJECTIVES 3.6: Numerical Integration LEARNING OBJECTIVES 3.6: Numerical Integration 106

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READ 3.6: Numerical Integration READ 3.6: Numerical Integration 107

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VIEW 3.6: Numerical Integration VIEW 3.6: Numerical Integration 108

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3.7 Improper Integrals 110

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LEARNING OBJECTIVES 3.7 Improper Integrals LEARNING OBJECTIVES 3.7 Improper Integrals 111

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READ 3.7 Improper Integrals READ 3.7 Improper Integrals 112

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VIEW 3.7 Improper Integrals VIEW 3.7 Improper Integrals 113

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EXERCISES 3.7- Improper Integrals EXERCISES 3.7- Improper Integrals 100 114

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Chapter 4 Introduction to Differential Equations 115

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4.1 Basics of Differential Equations 116

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LEARNING OBJECTIVES 4.1 Basics of Differential Equations LEARNING OBJECTIVES 4.1 Basics of Differential Equations 117

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READ 4.1 Basics of Differential Equations READ 4.1 Basics of Differential Equations 118

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VIEW 4.1 Basics of Differential Equations VIEW 4.1 Basics of Differential Equations 119

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4.2: Direction Fields and Numerical Methods 121

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LEARNING OBJECTIVES 4.2: Direction Fields and Numerical Methods LEARNING OBJECTIVES 4.2: Direction Fields and Numerical Methods 122

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READ 4.2: Direction Fields and Numerical Methods READ 4.2: Direction Fields and Numerical Methods 123

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VIEW 4.2: Direction Fields and Numerical Methods VIEW 4.2: Direction Fields and Numerical Methods 124

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4.3 Separable Equations 126

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LEARNING OBJECTIVES 4.3 Separable Equations LEARNING OBJECTIVES 4.3 Separable Equations 127

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READ 4.3 Separable Equations READ 4.3 Separable Equations 128

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VIEW 4.3 Separable Equations VIEW 4.3 Separable Equations 129

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4.4 The Logistic Equation 131

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LEARNING OBJECTIVES 4.4 The Logistic Equation LEARNING OBJECTIVES 4.4 The Logistic Equation 132

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READ 4.4 The Logistic Equation READ 4.4 The Logistic Equation 133

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VIEW 4.4 The Logistic Equation VIEW 4.4 The Logistic Equation 134

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4.5 First-order Linear Equations 136

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LEARNING OBJECTIVES 4.5 First-order Linear Equations LEARNING OBJECTIVES 4.5 First-order Linear Equations 137

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READ 4.5 First-order Linear Equations READ 4.5 First-order Linear Equations 138

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VIEW 4.5 First-order Linear Equations VIEW 4.5 First-order Linear Equations 139

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Chapter 5 Sequences and Series 141

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5.1 Sequences 142

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LEARNING OBJECTIVES 5.1 Sequences LEARNING OBJECTIVES 5.1 Sequences 143

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READ 5.1 Sequences READ 5.1 Sequences 144

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VIEW 5.1 Sequences VIEW 5.1 Sequences 145

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EXERCISES 5.1 Sequences EXERCISES 5.1 Sequences 100 146

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5.2 Infinite Series 147

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LEARNING OBJECTIVES 5.2 Infinite Series LEARNING OBJECTIVES 5.2 Infinite Series 148

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READ 5.2 Infinite Series READ 5.2 Infinite Series 149

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VIEW 5.2 Infinite Series VIEW 5.2 Infinite Series 150

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EXERCISES 5.2 Infinite Series EXERCISES 5.2 Infinite Series 150 151

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5.3 The Divergence and Integral Tests 152

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LEARNING OBJECTIVES 5.3 The Divergence and Integral Tests LEARNING OBJECTIVES 5.3 The Divergence and Integral Tests 153

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READ 5.3 The Divergence and Integral Tests READ 5.3 The Divergence and Integral Tests 154

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VIEW 5.3 The Divergence and Integral Tests VIEW 5.3 The Divergence and Integral Tests 155

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EXERCSIES 5.3 The Divergence and Integral Tests EXERCSIES 5.3 The Divergence and Integral Tests 120 156

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5.4 Comparison Tests 157

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LEARNING OBJECTIVES 5.4 Comparison Tests LEARNING OBJECTIVES 5.4 Comparison Tests 158

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READ 5.4 Comparison Tests READ 5.4 Comparison Tests 159

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VIEW 5.4 Comparison Tests VIEW 5.4 Comparison Tests 160

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EXERCISES 5.4 Comparison Tests EXERCISES 5.4 Comparison Tests 100 161

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5.5 Alternating Series 162

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LEARNING OBJECTIVES 5.5 Alternating Series LEARNING OBJECTIVES 5.5 Alternating Series 163

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READ 5.5 Alternating Series READ 5.5 Alternating Series 164

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VIEW 5.5 Alternating Series VIEW 5.5 Alternating Series 165

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EXERCISES 5.5 Alternating Series EXERCISES 5.5 Alternating Series 140 166

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5.6 Ratio and Root Tests 167

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LEARNING OBJECTIVES 5.6 Ratio and Root Tests LEARNING OBJECTIVES 5.6 Ratio and Root Tests 168

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READ 5.6 Ratio and Root Tests READ 5.6 Ratio and Root Tests 169

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VIEW 5.6 Ratio and Root Tests VIEW 5.6 Ratio and Root Tests 170

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EXERCISES 5.6 Ratio and Root Tests EXERCISES 5.6 Ratio and Root Tests 100 171

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Chapter 6 Power Series 172

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6.1 Power Series and Functions 173

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LEARNING OBJECTIVES 6.1 Power Series and Functions LEARNING OBJECTIVES 6.1 Power Series and Functions 174

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READ 6.1 Power Series and Functions READ 6.1 Power Series and Functions 175

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VIEW 6.1 Power Series and Functions VIEW 6.1 Power Series and Functions 176

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EXERCISES 6.1 Power Series and Functions EXERCISES 6.1 Power Series and Functions 150 177

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6.2 Properties of Power Series 178

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LEARNING OBJECTIVES 6.2 Properties of Power Series LEARNING OBJECTIVES 6.2 Properties of Power Series 179

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READ 6.2 Properties of Power Series READ 6.2 Properties of Power Series 180

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VIEW 6.2 Properties of Power Series VIEW 6.2 Properties of Power Series 181

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EXERCISES 6.2 Properties of Power Series EXERCISES 6.2 Properties of Power Series 150 182

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6.3 Taylor and Maclaurin Series 183

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LEARNING OBJECTIVES 6.3 Taylor and Maclaurin Series LEARNING OBJECTIVES 6.3 Taylor and Maclaurin Series 184

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READ 6.3 Taylor and Maclaurin Series READ 6.3 Taylor and Maclaurin Series 185

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VIEW 6.3 Taylor and Maclaurin Series VIEW 6.3 Taylor and Maclaurin Series 186

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Assignment

Exercises 6.3: Taylor & MacLaurin Series Exercises 6.3: Taylor & MacLaurin Series 130 187

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6.4: Working with Taylor Series 188

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LEARNING OBJECTIVES 6.4: Working with Taylor Series LEARNING OBJECTIVES 6.4: Working with Taylor Series 189

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READ 6.4: Working with Taylor Series READ 6.4: Working with Taylor Series 190

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VIEW 6.4: Working with Taylor Series VIEW 6.4: Working with Taylor Series 191

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Chapter 7 Parametric Equations and Polar Coordinates 193

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7.1 Parametric Equations 194

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LEARNING OBJECTIVES 7.1 Parametric Equations LEARNING OBJECTIVES 7.1 Parametric Equations 195

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READ 7.1 Parametric Equations READ 7.1 Parametric Equations 196

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VIEW 7.1 Parametric Equations VIEW 7.1 Parametric Equations 197

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Assignment

Exercises 7.1: Parametric Equations Exercises 7.1: Parametric Equations 190 198

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7.2 Calculus of Parametric Curves 199

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LEARNING OBJECTIVES 7.2 Calculus of Parametric Curves LEARNING OBJECTIVES 7.2 Calculus of Parametric Curves 200

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READ 7.2 Calculus of Parametric Curves READ 7.2 Calculus of Parametric Curves 201

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VIEW 7.2 Calculus of Parametric Curves VIEW 7.2 Calculus of Parametric Curves 202

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7.3 Polar Coordinates 204

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LEARNING OBJECTIVES 7.3 Polar Coordinates LEARNING OBJECTIVES 7.3 Polar Coordinates 205

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READ 7.3 Polar Coordinates READ 7.3 Polar Coordinates 206

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VIEW 7.3 Polar Coordinates VIEW 7.3 Polar Coordinates 207

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Exercises 7.3: Polar Coordinates Exercises 7.3: Polar Coordinates 140 208

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7.4 Area and Arc Length in Polar Coordinates 209

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LEARNING OBJECTIVES 7.4 Area and Arc Length in Polar Coordinates LEARNING OBJECTIVES 7.4 Area and Arc Length in Polar Coordinates 210

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READ 7.4 Area and Arc Length in Polar Coordinates READ 7.4 Area and Arc Length in Polar Coordinates 211

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VIEW 7.4 Area and Arc Length in Polar Coordinates VIEW 7.4 Area and Arc Length in Polar Coordinates 212

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Landing Page

Landing Page Landing Page

Page

Welcome to Calculus 2 Welcome to Calculus 2 1

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Welcome to Calculus 2 (Alternative Front Page) Welcome to Calculus 2 (Alternative Front Page) 2

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Chapter 1

Chapter 1 Chapter 1

Context Module Sub Header

Chapter Readings 1

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1 Introduction 1 Introduction 2

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1.1 Approximating Areas 1.1 Approximating Areas 3

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1.2 The Definite Integral 1.2 The Definite Integral 4

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1.3 The Fundamental Theorem of Calculus 1.3 The Fundamental Theorem of Calculus 5

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1.4 Integration Formulas and the Net Change Theorem 1.4 Integration Formulas and the Net Change Theorem 6

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1.5 Substitution 1.5 Substitution 7

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1.6 Integrals Involving Exponential and Logarithmic Functions 1.6 Integrals Involving Exponential and Logarithmic Functions 8

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1.7 Integrals Resulting in Inverse Trigonometric Functions 1.7 Integrals Resulting in Inverse Trigonometric Functions 9

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Chapter 2

Chapter 2 Chapter 2

Context Module Sub Header

Chapter Readings 1

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2 Introduction 2 Introduction 2

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2.1 Areas between Curves 2.1 Areas between Curves 3

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2.2 Determining Volumes by Slicing 2.2 Determining Volumes by Slicing 4

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2.3 Volumes of Revolution: Cylindrical Shells 2.3 Volumes of Revolution: Cylindrical Shells 5

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2.4 Arc Length of a Curve and Surface Area 2.4 Arc Length of a Curve and Surface Area 6

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2.5 Physical Applications 2.5 Physical Applications 7

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2.6 Moments and Centers of Mass 2.6 Moments and Centers of Mass 8

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2.7 Integrals, Exponential Functions, and Logarithms 2.7 Integrals, Exponential Functions, and Logarithms 9

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2.8 Exponential Growth and Decay 2.8 Exponential Growth and Decay 10

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2.9 Calculus of the Hyperbolic Functions 2.9 Calculus of the Hyperbolic Functions 11

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Chapter 3

Chapter 3 Chapter 3

Context Module Sub Header

Chapter Readings 1

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3 Introduction 3 Introduction 2

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3.1 Integration by Parts 3.1 Integration by Parts 3

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3.2 Trigonometric Integrals 3.2 Trigonometric Integrals 4

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3.3 Trigonometric Substitution 3.3 Trigonometric Substitution 5

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3.4 Partial Fractions 3.4 Partial Fractions 6

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3.5 Other Strategies for Integration 3.5 Other Strategies for Integration 7

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3.6 Numerical Integration 3.6 Numerical Integration 8

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3.7 Improper Integrals 3.7 Improper Integrals 9

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Chapter 4

Chapter 4 Chapter 4

Context Module Sub Header

Chapter Readings 1

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4 Introduction 4 Introduction 2

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4.1 Basics of Differential Equations 4.1 Basics of Differential Equations 3

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4.2 Direction Fields and Numerical Methods 4.2 Direction Fields and Numerical Methods 4

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4.3 Separable Equations 4.3 Separable Equations 5

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4.4 The Logistic Equation 4.4 The Logistic Equation 6

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4.5 First-order Linear Equations 4.5 First-order Linear Equations 7

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Chapter 5

Chapter 5 Chapter 5

Context Module Sub Header

Chapter Readings 1

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5 Introduction 5 Introduction 2

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5.1 Sequences 5.1 Sequences 3

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5.2 Infinite Series 5.2 Infinite Series 4

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5.3 The Divergence and Integral Tests 5.3 The Divergence and Integral Tests 5

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5.4 Comparison Tests 5.4 Comparison Tests 6

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5.5 Alternating Series 5.5 Alternating Series 7

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5.6 Ratio and Root Tests 5.6 Ratio and Root Tests 8

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Chapter 6

Chapter 6 Chapter 6

Context Module Sub Header

Chapter Readings 1

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6 Introduction 6 Introduction 2

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6.1 Power Series and Functions 6.1 Power Series and Functions 3

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6.2 Properties of Power Series 6.2 Properties of Power Series 4

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6.3 Taylor and Maclaurin Series 6.3 Taylor and Maclaurin Series 5

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6.4 Working with Taylor Series 6.4 Working with Taylor Series 6

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Chapter 7

Chapter 7 Chapter 7

Context Module Sub Header

Chapter Readings 1

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7 Introduction 7 Introduction 2

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7.1 Parametric Equations 7.1 Parametric Equations 3

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7.2 Calculus of Parametric Curves 7.2 Calculus of Parametric Curves 4

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External Url

7.3 Polar Coordinates 7.3 Polar Coordinates 5

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7.4 Area and Arc Length in Polar Coordinates 7.4 Area and Arc Length in Polar Coordinates 6

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7.5 Conic Sections 7.5 Conic Sections 7

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Table of Integrals Table of Integrals 8

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Table of Derivatives Table of Derivatives 9

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Review of Pre-Calculus Review of Pre-Calculus 10

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Course Modules

Week6 Lecture Notes

Imported Content

Week5 Lecture Notes

Week4 Lecture Notes

Week3 Lecture Notes

Week2 Lecture Notes

Week 1 Lecture Notes

Calc 2

1.1 Approximating Areas 1

1.2 The Definite Integral 7

1.3 The Fundamental Theorem of Calculus 12

1.4 Integration Formulas and the Net Change Theorem 17

1.5 Substitution 22

1.6 Integrals Involving Exponential and Logarithmic Functions 28

1.7 Integrals Resulting in Inverse Trigonometric Functions 33

Chapter 2 Applications of Integration 38

2.1 Areas Between Curves 39

2.2 Determining Volumes by Slicing 44

2.3 Volumes of Revolution: Cylindrical Shells 49

2.4 Arc Length of a Curve and Surface Area 54

2.5 Physical Applications 59

2.6 Moments and Centers of Mass 64

2.7 Integrals, Exponential Functions, and Logarithms 69

2.8 Exponential Growth and Decay 74

2.9 Calculus of the Hyperbolic Functions 79

Chapter 3 Techniques of Integration 84

3.1 Integration by Parts 85

3.2 Trigonometric Integrals 90

3.3 Trigonometric Substitution 95

3.4 Partial Fractions 100

3.6 Numerical Integration 105

3.7 Improper Integrals 110

Chapter 4 Introduction to Differential Equations 115

4.1 Basics of Differential Equations 116

4.2: Direction Fields and Numerical Methods 121

4.3 Separable Equations 126

4.4 The Logistic Equation 131

4.5 First-order Linear Equations 136

Chapter 5 Sequences and Series 141

5.1 Sequences 142

5.2 Infinite Series 147

5.3 The Divergence and Integral Tests 152

5.4 Comparison Tests 157

5.5 Alternating Series 162

5.6 Ratio and Root Tests 167

Chapter 6 Power Series 172

6.1 Power Series and Functions 173

6.2 Properties of Power Series 178

6.3 Taylor and Maclaurin Series 183

6.4: Working with Taylor Series 188

Chapter 7 Parametric Equations and Polar Coordinates 193

7.1 Parametric Equations 194

7.2 Calculus of Parametric Curves 199

7.3 Polar Coordinates 204

7.4 Area and Arc Length in Polar Coordinates 209

Landing Page

Chapter 1

Chapter Readings 1

Chapter 2

Chapter Readings 1

Chapter 3

Chapter Readings 1

Chapter 4

Chapter Readings 1

Chapter 5

Chapter Readings 1

Chapter 6

Chapter Readings 1

Chapter 7

Chapter Readings 1