com 1 , 0 0 1 Ca l c u l u s t i ce Pr o b l e m s Prac www.com 1 , 0 0 1 Ca lc ul u s t i ce Pr o b le m s Prac by PatrickJMT www.com 1,001 Calculus Practice Problems For Dummies® , Published by: John Wiley & Sons, Inc., Hoboken, NJ 07030-5774, www.com Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey Media and software compilation copyright © 2014 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.com/go/permissions.
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Library of Congress Control Number: 2013954232 ISBN 978-1-118-49671-8 (pbk); ISBN 978-1-118-49670-1 (ebk); ISBN 978-1-118-49673-2 (ebk) Manufactured in the United States of America 10 9 8 7 6 5 4 3 2 1 www.com 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.com Table of Contents Introduction. 1 What You’ll Find.
1 Beyond the Book. 1 What you’ll find online. 2 How to register. 2 Where to Go for Additional Help.
2 Part I: The Questions. 5 Chapter 1: Algebra Review. 7 The Problems You’ll Work On. 7 What to Watch Out For.
8 Writing Exponents Using Radical Notation. 9 The Horizontal Line Test. 9 Find Inverses Algebraically. 9 The Domain and Range of a Function and Its Inverse.
10 Solving Polynomial Equations by Factoring. 11 Absolute Value Equations. 11 Solving Rational Equations. 11 Polynomial and Rational Inequalities.
12 Absolute Value Inequalities. 12 Graphing Common Functions. 12 Domain and Range from a Graph. 13 End Behavior of Polynomials.
15 Long Division of Polynomials. 15 Chapter 2: Trigonometry Review. 17 The Problems You’ll Work On. 17 What to Watch Out For.
18 Converting Degree Measure to Radian Measure. 18 Converting Radian Measure to Degree Measure. 19 Finding Angles in the Coordinate Plane. 19 Finding Common Trigonometric Values.
21 Simplifying Trigonometric Expressions. 21 Solving Trigonometric Equations.com viii 1,001 Calculus Practice Problems For Dummies Amplitude, Period, Phase Shift, and Midline. 23 Equations of Periodic Functions. 23 Inverse Trigonometric Function Basics.
26 Solving Trigonometric Equations using Inverses. 26 Chapter 3: Limits and Rates of Change. 29 The Problems You’ll Work On. 29 What to Watch Out For.
29 Finding Limits from Graphs. 31 Applying the Squeeze Theorem. 32 Evaluating Trigonometric Limits. 33 Limits from Graphs.
36 Limits at Infinity. 38 Continuity and Discontinuities. 39 Making a Function Continuous. 40 The Intermediate Value Theorem.
41 Chapter 4: Derivative Basics. 43 The Problems You’ll Work On. 43 What to Watch Out For. 43 Determining Differentiability from a Graph.
44 Finding the Derivative by Using the Definition. 45 Finding the Value of the Derivative Using a Graph. 46 Using the Power Rule to Find Derivatives. 47 Finding All Points on a Graph Where Tangent Lines Have a Given Value.
48 Chapter 5: The Product, Quotient, and Chain Rules. 49 The Problems You’ll Work On. 49 What to Watch Out For. 49 Using the Product Rule to Find Derivatives.
50 Using the Quotient Rule to Find Derivatives. 51 Using the Chain Rule to Find Derivatives. 52 More Challenging Chain Rule Problems. 53 Chapter 6: Exponential and Logarithmic Functions and Tangent Lines.
55 The Problems You’ll Work On. 55 What to Watch Out For. 55 Derivatives Involving Logarithmic Functions. 56 Logarithmic Differentiation to Find the Derivative.
56 Finding Derivatives of Functions Involving Exponential Functions. 57 Finding Equations of Tangent Lines. 57 Finding Equations of Normal Lines.com Table of Contents ix Chapter 7: Implicit Differentiation. 59 The Problems You’ll Work On.
59 What to Watch Out For. 59 Using Implicit Differentiation to Find a Derivative. 60 Using Implicit Differentiation to Find a Second Derivative. 60 Finding Equations of Tangent Lines Using Implicit Differentiation.
61 Chapter 8: Applications of Derivatives. 63 The Problems You’ll Work On. 63 What to Watch Out For. 63 Finding and Evaluating Differentials.
64 Using Linearizations to Estimate Values. 64 Understanding Related Rates. 64 Finding Maxima and Minima from Graphs. 66 Using the Closed Interval Method.
67 Finding Intervals of Increase and Decrease. 68 Using the First Derivative Test to Find Local Maxima and Minima. 68 Identifying Inflection Points. 69 Using the Second Derivative Test to Find Local Maxima and Minima.
69 Applying Rolle’s Theorem. 69 Using the Mean Value Theorem. 70 Applying the Mean Value Theorem to Solve Problems. 70 Relating Velocity and Position.
70 Finding Velocity and Speed. 70 Solving Optimization Problems. 71 Doing Approximations Using Newton’s Method. 73 Approximating Roots Using Newton’s Method.
73 Chapter 9: Areas and Riemann Sums. 75 The Problems You’ll Work On. 75 What to Watch Out For. 75 Calculating Riemann Sums Using Left Endpoints.
76 Calculating Riemann Sums Using Right Endpoints. 76 Calculating Riemann Sums Using Midpoints. 77 Using Limits and Riemann Sums to Find Expressions for Definite Integrals. 77 Finding a Definite Integral from the Limit and Riemann Sum Form.
78 Using Limits and Riemann Sums to Evaluate Definite Integrals.com x 1,001 Calculus Practice Problems For Dummies Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem. 79 The Problems You’ll Work On. 79 What to Watch Out For. 79 Using the Fundamental Theorem of Calculus to Find Derivatives.
80 Working with Basic Examples of Definite Integrals. 80 Understanding Basic Indefinite Integrals. 81 Understanding the Net Change Theorem. 84 Finding the Displacement of a Particle Given the Velocity.
85 Finding the Distance Traveled by a Particle Given the Velocity. 85 Finding the Displacement of a Particle Given Acceleration. 86 Finding the Distance Traveled by a Particle Given Acceleration. 86 Chapter 11: Applications of Integration.
87 The Problems You’ll Work On. 87 What to Watch Out For. 87 Areas between Curves. 88 Finding Volumes Using Disks and Washers.
89 Finding Volume Using Cross-Sectional Slices. 91 Finding Volumes Using Cylindrical Shells. 94 Average Value of a Function. 97 Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L’Hôpital’s Rule.
99 The Problems You’ll Work On. 99 What to Watch Out For. 99 Finding Derivatives Involving Inverse Trigonometric Functions. 100 Finding Antiderivatives by Using Inverse Trigonometric Functions.
101 Evaluating Hyperbolic Functions Using Their Definitions. 101 Finding Derivatives of Hyperbolic Functions. 102 Finding Antiderivatives of Hyperbolic Functions. 102 Evaluating Indeterminate Forms Using L’Hôpital’s Rule.
103 Chapter 13: U-Substitution and Integration by Parts. 107 The Problems You’ll Work On. 107 What to Watch Out For. 108 Using Integration by Parts.com Table of Contents xi Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions.
113 The Problems You’ll Work On. 113 What to Watch Out For. 116 Finding Partial Fraction Decompositions (without Coefficients). 117 Finding Partial Fraction Decompositions (Including Coefficients).
118 Integrals Involving Partial Fractions. 119 Chapter 15: Improper Integrals and More Approximating Techniques. 121 The Problems You’ll Work On. 121 What to Watch Out For.
121 Convergent and Divergent Improper Integrals. 122 The Comparison Test for Integrals. 123 The Trapezoid Rule. 124 Part II: The Answers.
125 Chapter 16: Answers and Explanations .com xii 1,001 Calculus Practice Problems For Dummies www.com Introduction T his book is intended for a variety of calculus students. Perhaps you want a supplement to your current calculus class or you’re looking to brush up on a course you took long ago. Or maybe you’re teaching yourself and need a comprehensive book of extra practice problems. The 1,001 questions in this book cover calculus concepts that a high school student would encounter in a calculus course in preparation for the AP exam.
It also covers most of the concepts that a calculus student could expect to see in the first two semesters of a three- semester calculus course. The types of questions are questions that I regularly assigned when teaching both as homework questions or are questions that a student could’ve expected to see on a quiz or test. Jump around the book as you like. You can find a robust algebra and trigonometry review at the beginning of the book to make sure that you’re prepared for calculus.
The number-one reason students have difficulty in calculus is not calculus itself but having a weak back- ground in algebra and trigonometry. If you’re rusty on the fundamentals, spend time on those first two chapters before jumping into the rest of the text! As with many things worth doing in life, there’s no shortcut to becoming proficient in mathematics. However, by practicing the problems in this book, you’ll be on your way to becoming a much stronger calculus student. What You’ll Find The 1,001 calculus practice problems in the book are divided into 15 chapters, with each chapter providing practice of the mechanical side of calculus or of applications of calcu- lus.
Some of the questions have a diagram or graph that you need in order to answer the question. The end of the book provides thorough and detailed solutions to all the problems. If you get an answer wrong, try again before reading the solution! Knowing what not to do is often a great starting point in discovering the correct approach, so don’t worry if you don’t immediately solve each question; some problems can be quite challenging. Beyond the Book This book provides a lot of calculus practice.