Calculus 1,001 practice problems for dummies

www.it-ebooks.info www.it-ebooks.info s u l u c l a C 0 , s m e l b o r P e c i t Prac www.it-ebooks.info www.it-ebooks.info s u l u c l a C 0 , s m e l b o r P e c i t Prac by PatrickJMT www.it-ebooks.info 1,001 Calculus Practice Problems For Dummies® , Published by: John Wiley & Sons, Inc., 111 River St., Hoboken, NJ 07030-5774, www.wiley.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.wiley.com/go/permissions Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and may not be used without written permission All other trademarks are the property of their respective owners John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: WHILE THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST EFFORTS IN PREPARING THIS BOOK, THEY MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS BOOK AND SPECIFICALLY DISCLAIM ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRESENTATIVES OR WRITTEN SALES MATERIALS THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR YOUR SITUATION YOU SHOULD CONSULT WITH A PROFESSIONAL WHERE APPROPRIATE NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM For general information on our other products and services, please contact our Customer Care Department within the U.S at 877-762-2974, outside the U.S at 317-572-3993, or fax 317-572-4002 For technical support, please visit www.wiley.com/techsupport Wiley publishes in a variety of print and electronic formats and by print-on-demand Some material included with standard print versions of this book may not be included in e-books or in print-on-demand If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com For more information about Wiley products, visit www.wiley.com 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 www.it-ebooks.info Contents at a Glance Introduction Part I: The Questions Chapter 1: Algebra Review 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 www.it-ebooks.info www.it-ebooks.info Table of Contents Introduction What You’ll Find Beyond the Book What you’ll find online How to register Where to Go for Additional Help Part I: The Questions Chapter 1: Algebra Review The Problems You’ll Work On What to Watch Out For Simplifying Fractions Simplifying Radicals Writing Exponents Using ­Radical Notation The Horizontal Line Test Find Inverses Algebraically The Domain and Range of a Function and Its Inverse 10 Linear Equations 10 Quadratic Equations 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 14 Adding Polynomials 14 Subtracting Polynomials 14 Multiplying Polynomials 15 Long Division of Polynomials 15 Chapter 2: Trigonometry Review 17 The Problems You’ll Work On 17 What to Watch Out For 17 Basic Trigonometry 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 22 www.it-ebooks.info 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 30 Evaluating Limits 31 Applying the Squeeze Theorem 32 Evaluating Trigonometric Limits 33 Infinite Limits 33 Limits from Graphs 36 Limits at Infinity 37 Horizontal Asymptotes 38 Classifying Discontinuities 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 58 www.it-ebooks.info ... information You can also head to www .dummies. com to see the many articles and books that can help you in your studies 1,001 Calculus Practice Problems For Dummies gives you just that — 1,001 practice. .. their companion workbooks): ✓ Calculus For Dummies: This book provides instruction parallel to the 1,001 calculus practice problems found here ✓ Calculus II For Dummies: This book provides content... xi xii 1,001 Calculus Practice Problems For Dummies www.it-ebooks.info Introduction T his book is intended for a variety of calculus students Perhaps you want a supplement to your current calculus