, Calculus
of a Single Variable
Ninth Edition
Ron Larson
The Pennsylvania State University
The Behrend College
Bruce H. Edwards
University of Florida
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
, Calculus of a Single Variable, Ninth Edition © 2010, 2006 Brooks/Cole, Cengage Learning
Larson/Edwards
ALL RIGHTS RESERVED. No part of this work covered by the copyright
VP/Editor-in-Chief: Michelle Julet herein may be reproduced, transmitted, stored or used in any form or by
Publisher: Richard Stratton any means graphic, electronic, or mechanical, including but not limited
to photocopying, recording, scanning, digitizing, taping, Web distribution,
Senior Sponsoring Editor: Cathy Cantin
information networks, or information storage and retrieval systems,
Development Editor: Peter Galuardi except as permitted under Section 107 or 108 of the 1976 United States
Associate Editor: Jeannine Lawless Copyright Act, without the prior written permission of the publisher.
Editorial Assistant: Amy Haines
Media Editor: Peter Galuardi For product information and technology assistance, contact us at
Senior Content Manager: Maren Kunert Cengage Learning Customer & Sales Support, 1-800-354-9706
Senior Marketing Manager: Jennifer Jones For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions.
Marketing Communications Manager: Mary Anne Payumo
Further permissions questions can be emailed to
Senior Content Project Manager, Editorial Production:
Tamela Ambush
Art and Design Manager: Jill Haber
Library of Congress Control Number: 2008933835
Senior Manufacturing Coordinator: Diane Gibbons
Student Edition:
Permissions Editor: Katie Huha
ISBN-13: 978-0-547-20998-2
Text Designer: Nesbitt Graphics
ISBN-10: 0-547-20998-3
Art Editor: Larson Texts, Inc.
Senior Photo Editor: Jennifer Meyer Dare
Brooks/Cole
Illustrator: Larson Texts, Inc.
10 Davis Drive
Cover Designer: Harold Burch Belmont, CA 94002-3098
Cover Image: © Richard Edelman/Woodstock Graphics Studio USA
Compositor: Larson Texts, Inc.
Cengage learning is a leading provider of customized learning solutions
TI is a registered trademark of Texas Instruments, Inc. with office locations around the globe, including Singapore, the United
Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at:
Mathematica is a registered trademark of Wolfram Research, Inc.
international.cengage.com/region
Maple is a registered trademark of Waterloo Maple, Inc.
Cengage learning products are represented in Canada by Nelson
Problems from the William Lowell Putnam Mathematical Education, Ltd.
Competition reprinted with permission from the Mathematical
Association of America, 1529 Eighteenth Street, NW.
For your course and learning solutions, visit www.cengage.com
Washington, DC.
Purchase any of our products at your local college store or at our
preferred online store www.ichapters.com
Printed in the United States of America
1 2 3 4 5 6 7 12 11 10 09 08
, C ontents
A Word from the Authors viii
Textbook Features xii
CHAPTER P Preparation for Calculus 1
P.1 Graphs and Models 2
P.2 Linear Models and Rates of Change 10
P.3 Functions and Their Graphs 19
P.4 Fitting Models to Data 31
Review Exercises 37
P.S. Problem Solving 39
CHAPTER 1 Limits and Their Properties 41
1.1 A Preview of Calculus 42
1.2 Finding Limits Graphically and Numerically 48
1.3 Evaluating Limits Analytically 59
1.4 Continuity and One-Sided Limits 70
1.5 Infinite Limits 83
S E C T I O N P R O J E C T: Graphs and Limits of
Trigonometric Functions 90
Review Exercises 91
P.S. Problem Solving 93
CHAPTER 2 Differentiation 95
2.1 The Derivative and the Tangent Line Problem 96
2.2 Basic Differentiation Rules and Rates of Change 107
2.3 Product and Quotient Rules and Higher-Order Derivatives 119
2.4 The Chain Rule 130
2.5 Implicit Differentiation 141
S E C T I O N P R O J E C T: Optical Illusions 148
2.6 Related Rates 149
Review Exercises 158
P.S. Problem Solving 161
iii
of a Single Variable
Ninth Edition
Ron Larson
The Pennsylvania State University
The Behrend College
Bruce H. Edwards
University of Florida
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
, Calculus of a Single Variable, Ninth Edition © 2010, 2006 Brooks/Cole, Cengage Learning
Larson/Edwards
ALL RIGHTS RESERVED. No part of this work covered by the copyright
VP/Editor-in-Chief: Michelle Julet herein may be reproduced, transmitted, stored or used in any form or by
Publisher: Richard Stratton any means graphic, electronic, or mechanical, including but not limited
to photocopying, recording, scanning, digitizing, taping, Web distribution,
Senior Sponsoring Editor: Cathy Cantin
information networks, or information storage and retrieval systems,
Development Editor: Peter Galuardi except as permitted under Section 107 or 108 of the 1976 United States
Associate Editor: Jeannine Lawless Copyright Act, without the prior written permission of the publisher.
Editorial Assistant: Amy Haines
Media Editor: Peter Galuardi For product information and technology assistance, contact us at
Senior Content Manager: Maren Kunert Cengage Learning Customer & Sales Support, 1-800-354-9706
Senior Marketing Manager: Jennifer Jones For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions.
Marketing Communications Manager: Mary Anne Payumo
Further permissions questions can be emailed to
Senior Content Project Manager, Editorial Production:
Tamela Ambush
Art and Design Manager: Jill Haber
Library of Congress Control Number: 2008933835
Senior Manufacturing Coordinator: Diane Gibbons
Student Edition:
Permissions Editor: Katie Huha
ISBN-13: 978-0-547-20998-2
Text Designer: Nesbitt Graphics
ISBN-10: 0-547-20998-3
Art Editor: Larson Texts, Inc.
Senior Photo Editor: Jennifer Meyer Dare
Brooks/Cole
Illustrator: Larson Texts, Inc.
10 Davis Drive
Cover Designer: Harold Burch Belmont, CA 94002-3098
Cover Image: © Richard Edelman/Woodstock Graphics Studio USA
Compositor: Larson Texts, Inc.
Cengage learning is a leading provider of customized learning solutions
TI is a registered trademark of Texas Instruments, Inc. with office locations around the globe, including Singapore, the United
Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at:
Mathematica is a registered trademark of Wolfram Research, Inc.
international.cengage.com/region
Maple is a registered trademark of Waterloo Maple, Inc.
Cengage learning products are represented in Canada by Nelson
Problems from the William Lowell Putnam Mathematical Education, Ltd.
Competition reprinted with permission from the Mathematical
Association of America, 1529 Eighteenth Street, NW.
For your course and learning solutions, visit www.cengage.com
Washington, DC.
Purchase any of our products at your local college store or at our
preferred online store www.ichapters.com
Printed in the United States of America
1 2 3 4 5 6 7 12 11 10 09 08
, C ontents
A Word from the Authors viii
Textbook Features xii
CHAPTER P Preparation for Calculus 1
P.1 Graphs and Models 2
P.2 Linear Models and Rates of Change 10
P.3 Functions and Their Graphs 19
P.4 Fitting Models to Data 31
Review Exercises 37
P.S. Problem Solving 39
CHAPTER 1 Limits and Their Properties 41
1.1 A Preview of Calculus 42
1.2 Finding Limits Graphically and Numerically 48
1.3 Evaluating Limits Analytically 59
1.4 Continuity and One-Sided Limits 70
1.5 Infinite Limits 83
S E C T I O N P R O J E C T: Graphs and Limits of
Trigonometric Functions 90
Review Exercises 91
P.S. Problem Solving 93
CHAPTER 2 Differentiation 95
2.1 The Derivative and the Tangent Line Problem 96
2.2 Basic Differentiation Rules and Rates of Change 107
2.3 Product and Quotient Rules and Higher-Order Derivatives 119
2.4 The Chain Rule 130
2.5 Implicit Differentiation 141
S E C T I O N P R O J E C T: Optical Illusions 148
2.6 Related Rates 149
Review Exercises 158
P.S. Problem Solving 161
iii
