CalcII_Complete_Problems.pdf - Practice Problems Paul Dawkins Calculus II \u2013 Practice Problems i Table of Contents Preface iii Outline iv Chapter 1

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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