CalcII_Complete_Problems.pdf - Practice Problems Paul...

Practice Problems
Paul Dawkins

Calculus II – Practice Problems i
© 2018 Paul Dawkins
Table of Contents
Preface ................................................................................................................................................................. iii
Outline .................................................................................................................................................................. iv
Chapter 1 : Integration Techniques ........................................................................................................................ 1
Section 1-1 : Integration by Parts .............................................................................................................................. 3
Section 1-2 : Integrals Involving Trig Functions ......................................................................................................... 4
Section 1-3 : Trig Substitutions .................................................................................................................................. 5
Section 1-4 : Partial Fractions .................................................................................................................................... 7
Section 1-5 : Integrals Involving Roots ...................................................................................................................... 8
Section 1-6 : Integrals Involving Quadratics .............................................................................................................. 9
Section 1-7 : Integration Strategy ........................................................................................................................... 10
Section 1-8 : Improper Integrals .............................................................................................................................. 11
Section 1-9 : Comparison Test for Improper Integrals ............................................................................................ 12
Section 1-10 : Approximating Definite Integrals ..................................................................................................... 13
Chapter 2 : Applications of Integrals .................................................................................................................... 14
Section 2-1 : Arc Length .......................................................................................................................................... 15
Section 2-2 : Surface Area ....................................................................................................................................... 16
Section 2-3 : Center of Mass ................................................................................................................................... 17
Section 2-4 : Hydrostatic Pressure and Force ......................................................................................................... 18
Section 2-5 : Probability .......................................................................................................................................... 20
Chapter 3 : Parametric Equations and Polar Coordinates ..................................................................................... 21
Section 3-1 : Parametric Equations and Curves ...................................................................................................... 23
Section 3-2 : Tangents with Parametric Equations ................................................................................................. 25
Section 3-3 : Area with Parametric Equations ......................................................................................................... 26
Section 3-4 : Arc Length with Parametric Equations ............................................................................................... 27
Section 3-5 : Surface Area with Parametric Equations ............................................................................................ 28
Section 3-6 : Polar Coordinates ............................................................................................................................... 29
Section 3-7 : Tangents with Polar Coordinates ....................................................................................................... 31
Section 3-8 : Area with Polar Coordinates .............................................................................................................. 32
Section 3-9 : Arc Length with Polar Coordinates ..................................................................................................... 33
Section 3-10 : Surface Area with Polar Coordinates ............................................................................................... 34
Section 3-11 : Arc Length and Surface Area Revisited ............................................................................................ 35
Chapter 4 : Series & Sequences ............................................................................................................................ 36
Section 4-1 : Sequences .......................................................................................................................................... 39
Section 4-2 : More on Sequences ............................................................................................................................ 40
Section 4-3 : Series - The Basics .............................................................................................................................. 41
Section 4-4 : Convergence/Divergence of Series .................................................................................................... 42
Section 4-5 : Special Series ...................................................................................................................................... 43
Section 4-6 : Integral Test ........................................................................................................................................ 44
Section 4-7 : Comparison Test/Limit Comparison Test ........................................................................................... 45
Section 4-8 : Alternating Series Test ....................................................................................................................... 46
Section 4-9 : Absolute Convergence ....................................................................................................................... 47
Section 4-10 : Ratio Test .......................................................................................................................................... 48
Section 4-11 : Root Test .......................................................................................................................................... 49
Section 4-12 : Strategy for Series ............................................................................................................................ 50

Calculus II – Practice Problems ii
© 2018 Paul Dawkins
Section 4-13 : Estimating the Value of a Series ....................................................................................................... 51
Section 4-14 : Power Series ..................................................................................................................................... 52
Section 4-15 : Power Series and Functions ............................................................................................................. 53
Section 4-16 : Taylor Series ..................................................................................................................................... 54
Section 4-17 : Applications of Series ....................................................................................................................... 55
Section 4-18 : Binomial Series ................................................................................................................................. 56
Chapter 5 : Vectors .............................................................................................................................................. 57
Section 5-1 : Vectors - The Basics ............................................................................................................................ 58
Section 5-2 : Vector Arithmetic ............................................................................................................................... 59
Section 5-3 : Dot Product ........................................................................................................................................ 60
Section 5-4 : Cross Product ..................................................................................................................................... 61
Chapter 6 : 3-Dimensional Space ......................................................................................................................... 62
Section 6-1 : The 3-D Coordinate System ................................................................................................................ 64
Section 6-2 : Equations of Lines .............................................................................................................................. 65
Section 6-3 : Equations of Planes ............................................................................................................................ 66
Section 6-4 : Quadric Surfaces ................................................................................................................................ 67
Section 6-5 : Functions of Several Variables ........................................................................................................... 68
Section 6-6 : Vector Functions ................................................................................................................................ 69
Section 6-7 : Calculus with Vector Functions .......................................................................................................... 70
Section 6-8 : Tangent, Normal and Binormal Vectors ............................................................................................. 71
Section 6-9 : Arc Length with Vector Functions ...................................................................................................... 72
Section 6-10 : Curvature .......................................................................................................................................... 73
Section 6-11 : Velocity and Acceleration ................................................................................................................. 74
Section 6-12 : Cylindrical Coordinates ..................................................................................................................... 75
Section 6-13 : Spherical Coordinates ...................................................................................................................... 76

Calculus II – Practice Problems iii
© 2018 Paul Dawkins
Preface
Here are a set of practice problems for the Calculus II notes. If you are viewing the pdf version