Contents at a Glance
Introduction ............................................................................ 1
Part I: The Questions ................................................................ 5
Chapter 1: Algebra Review .................................................................................................................. 7
Chapter 2: Trigonometry Review ...................................................................................................... 17
Chapter 3: Limits and Rates of Change ............................................................................................ 29
Chapter 4: Derivative Basics ............................................................................................................. 43
Chapter 5: The Product, Quotient, and Chain Rules ...................................................................... 49
Chapter 6: Exponential and Logarithmic Functions and Tangent Lines ...................................... 55
Chapter 7: Implicit Differentiation .................................................................................................... 59
Chapter 8: Applications of Derivatives ............................................................................................ 63
Chapter 9: Areas and Riemann Sums ............................................................................................... 75
Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem.................. 79
Chapter 11: Applications of Integration ........................................................................................... 87
Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions,
and L’Hôpital’s Rule ......................................................................................................................... 99
Chapter 13: U-Substitution and Integration by Parts ................................................................... 107
Chapter 14: Trigonometric Integrals, Trigonometric Substitution,
and Partial Fractions...................................................................................................................... 113
Chapter 15: Improper Integrals and More Approximating Techniques ..................................... 121
Part II: The Answers ............................................................ 125
Chapter 16: Answers and Explanations ......................................................................................... 127
Index .................................................................................. 595
Introduction ............................................................................ 1
Part I: The Questions ................................................................ 5
Chapter 1: Algebra Review .................................................................................................................. 7
Chapter 2: Trigonometry Review ...................................................................................................... 17
Chapter 3: Limits and Rates of Change ............................................................................................ 29
Chapter 4: Derivative Basics ............................................................................................................. 43
Chapter 5: The Product, Quotient, and Chain Rules ...................................................................... 49
Chapter 6: Exponential and Logarithmic Functions and Tangent Lines ...................................... 55
Chapter 7: Implicit Differentiation .................................................................................................... 59
Chapter 8: Applications of Derivatives ............................................................................................ 63
Chapter 9: Areas and Riemann Sums ............................................................................................... 75
Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem.................. 79
Chapter 11: Applications of Integration ........................................................................................... 87
Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions,
and L’Hôpital’s Rule ......................................................................................................................... 99
Chapter 13: U-Substitution and Integration by Parts ................................................................... 107
Chapter 14: Trigonometric Integrals, Trigonometric Substitution,
and Partial Fractions...................................................................................................................... 113
Chapter 15: Improper Integrals and More Approximating Techniques ..................................... 121
Part II: The Answers ............................................................ 125
Chapter 16: Answers and Explanations ......................................................................................... 127
Index .................................................................................. 595