Adskdkeofprper

CA L C U L U S
E A R LY T R A N S C E N D E N TA L S
SIXTH EDITION

JAMES STEWART
McMASTER UNIVERSITY

AUSTRALIA

N

BRAZIL

N

C A N A DA

N

MEXICO

N

SINGAPORE

N

S PA I N

N

UNITED KINGDOM

N

U N I T E D S TAT E S

Calculus Early Transcendentals, 6e James Stewart
Publisher Bob Pirtle Assistant Editor Stacy Green Editorial Assistant Elizabeth RodioTechnology Project Manager Sam Subity Marketing Manager Mark Santee Marketing Assistant Melissa Wong Marketing Communications Manager Bryan Vann Project Manager, Editorial Production Cheryll Linthicum Creative Director Rob Hugel Art Director Vernon T. Boes Print Buyer Becky Cross
N N N N N N N N N N N

Permissions Editor Bob Kauser Production Service TECH·arts Text Designer Kathi Townes PhotoResearcher Stephanie Kuhns Copy Editor Kathi Townes Illustrator Brian Betsill Cover Designer Irene Morris Cover Image Amelie Fear, Folkmusician.com Cover Printer R. R. Donnelley /Willard Compositor Stephanie Kuhns, TECH·arts Printer R. R. Donnelley /Willard
N N N N N N N N N N N

COPYRIGHT © 2008, 2003 Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Coleare trademarks used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner—without the written permission of the publisher. Printed in theUnited States of America 1 2 3 4 5 6 7 11 10 09 08 07

Trademarks ExamView ® and ExamViewPro ® are registered trademarks of FSCreations, Inc. Windows is a registered trademark of the Microsoft Corporation and used herein under license. Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc. Used herein under license. Derive is a registered trademark of Soft Warehouse, Inc.Maple is a registered trademark of Waterloo Maple, Inc. Mathematica is a registered trademark of Wolfram Research, Inc. Tools for Enriching is a trademark used herein under license. Thomson Higher Education 10 Davis Drive Belmont, CA 94002 USA

For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563 For permission to use material from thistext or product, submit a request online at http://www.thomsonrights.com Any additional questions about permissions can be submitted by email to thomsonrights@thomson.com.

© 2008 Thomson Learning, Inc. All Rights Reserved. Thomson Learning WebTutor™ is a trademark of Thomson Learning, Inc. Library of Congress Control Number: 2006939532 ISBN-13: 978-0-495-01166-8 ISBN-10: 0-495-01166-5
K05T07CONTENTS
Preface xi xxiii xxiv
2

To the Student Diagnostic Tests

A PREVIEW OF C ALCULUS

1

FUNCTIONS AND MODELS
1.1 1.2 1.3 1.4 1.5 1.6

10

Four Ways to Represent a Function New Functions from Old Functions Graphing Calculators and Computers Exponential Functions Review 73 52 Inverse Functions and Logarithms

11 24 37 46 59

Mathematical Models: A Catalog of EssentialFunctions

Principles of Problem Solving

76

2

LIMITS AND DERIVATIVES

82

2.1 2.2 2.3 2.4 2.5 2.6 2.7

The Tangent and Velocity Problems The Limit of a Function 88

83 99

Calculating Limits Using the Limit Laws The Precise Definition of a Limit Continuity 119 109

Limits at Infinity; Horizontal Asymptotes Derivatives and Rates of Change 143 Writing Project Early Methods forFinding Tangents
N

130
153

2.8

The Derivative as a Function Review 165

154

Problems Plus

170

iii

iv

||||

CONTENTS

3
m=0 m=1 0
π 2

DIFFERENTIATION RULES
3.1

172

Derivatives of Polynomials and Exponential Functions
Applied Project Building a Better Roller Coaster
N

173

m=_1 π

182

3.2 3.3 3.4

The Product and Quotient Rules The Chain Rule...