,THOMAS’
CALCULUS
EARLY TRANSCENDENTALS
Twelfth Edition
Based on the original work by
George B. Thomas, Jr.
Massachusetts Institute of Technology
as revised by
Maurice D. Weir
Naval Postgraduate School
Joel Hass
University of California, Davis
,Editor-in-Chief: Deirdre Lynch
Senior Acquisitions Editor: William Hoffman
Senior Project Editor: Rachel S. Reeve
Associate Editor: Caroline Celano
Associate Project Editor: Leah Goldberg
Senior Managing Editor: Karen Wernholm
Senior Production Project Manager: Sheila Spinney
Senior Design Supervisor: Andrea Nix
Digital Assets Manager: Marianne Groth
Media Producer: Lin Mahoney
Software Development: Mary Durnwald and Bob Carroll
Executive Marketing Manager: Jeff Weidenaar
Marketing Assistant: Kendra Bassi
Senior Author Support/Technology Specialist: Joe Vetere
Senior Prepress Supervisor: Caroline Fell
Manufacturing Manager: Evelyn Beaton
Production Coordinator: Kathy Diamond
Composition: Nesbitt Graphics, Inc.
Illustrations: Karen Heyt, IllustraTech
Cover Design: Rokusek Design
Cover image: Forest Edge, Hokuto, Hokkaido, Japan 2004 © Michael Kenna
About the cover: The cover image of a tree line on a snow-swept landscape, by the photographer Michael Kenna,
was taken in Hokkaido, Japan. The artist was not thinking of calculus when he composed the image, but rather, of a
visual haiku consisting of a few elements that would spark the viewer’s imagination. Similarly, the minimal design
of this text allows the central ideas of calculus developed in this book to unfold to ignite the learner’s imagination.
For permission to use copyrighted material, grateful acknowledgment is made to the copyright holders on page C-1,
which is hereby made part of this copyright page.
Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks.
Where those designations appear in this book, and Addison-Wesley was aware of a trademark claim, the designa-
tions have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Weir, Maurice D.
Thomas’ calculus : early transcendentals / Maurice D. Weir, Joel Hass, George B. Thomas.—12th ed.
p. cm
Includes index.
ISBN 978-0-321-58876-0
1. Calculus—Textbooks. 2. Geometry, Analytic—Textbooks. I. Hass, Joel. II. Thomas, George B. (George
Brinton), 1914–2006. III. Title IV. Title: Calculus.
QA303.2.W45 2009
515—dc22 2009023070
Copyright © 2010, 2006, 2001 Pearson Education, Inc. All rights reserved. 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, or otherwise, without the prior written permission of the publisher. Printed in the United
States of America. For information on obtaining permission for use of material in this work, please submit a written
request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA
02116, fax your request to 617-848-7047, or e-mail at http://www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—CRK—12 11 10 09
ISBN-10: 0-321-58876-2
www.pearsoned.com ISBN-13: 978-0-321-58876-0
, CONTENTS
Preface ix
Functions 1
1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 14
1.3 Trigonometric Functions 22
1.4 Graphing with Calculators and Computers 30
1.5 Exponential Functions 34
1.6 Inverse Functions and Logarithms 40
QUESTIONS TO GUIDE YOUR REVIEW 52
PRACTICE EXERCISES 53
ADDITIONAL AND ADVANCED EXERCISES 55
Limits and Continuity 58
2
2.1 Rates of Change and Tangents to Curves 58
2.2 Limit of a Function and Limit Laws 65
2.3 The Precise Definition of a Limit 76
2.4 One-Sided Limits 85
2.5 Continuity 92
2.6 Limits Involving Infinity; Asymptotes of Graphs 103
QUESTIONS TO GUIDE YOUR REVIEW 116
PRACTICE EXERCISES 117
ADDITIONAL AND ADVANCED EXERCISES 119
Differentiation 122
3
3.1 Tangents and the Derivative at a Point 122
3.2 The Derivative as a Function 126
iii
CALCULUS
EARLY TRANSCENDENTALS
Twelfth Edition
Based on the original work by
George B. Thomas, Jr.
Massachusetts Institute of Technology
as revised by
Maurice D. Weir
Naval Postgraduate School
Joel Hass
University of California, Davis
,Editor-in-Chief: Deirdre Lynch
Senior Acquisitions Editor: William Hoffman
Senior Project Editor: Rachel S. Reeve
Associate Editor: Caroline Celano
Associate Project Editor: Leah Goldberg
Senior Managing Editor: Karen Wernholm
Senior Production Project Manager: Sheila Spinney
Senior Design Supervisor: Andrea Nix
Digital Assets Manager: Marianne Groth
Media Producer: Lin Mahoney
Software Development: Mary Durnwald and Bob Carroll
Executive Marketing Manager: Jeff Weidenaar
Marketing Assistant: Kendra Bassi
Senior Author Support/Technology Specialist: Joe Vetere
Senior Prepress Supervisor: Caroline Fell
Manufacturing Manager: Evelyn Beaton
Production Coordinator: Kathy Diamond
Composition: Nesbitt Graphics, Inc.
Illustrations: Karen Heyt, IllustraTech
Cover Design: Rokusek Design
Cover image: Forest Edge, Hokuto, Hokkaido, Japan 2004 © Michael Kenna
About the cover: The cover image of a tree line on a snow-swept landscape, by the photographer Michael Kenna,
was taken in Hokkaido, Japan. The artist was not thinking of calculus when he composed the image, but rather, of a
visual haiku consisting of a few elements that would spark the viewer’s imagination. Similarly, the minimal design
of this text allows the central ideas of calculus developed in this book to unfold to ignite the learner’s imagination.
For permission to use copyrighted material, grateful acknowledgment is made to the copyright holders on page C-1,
which is hereby made part of this copyright page.
Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks.
Where those designations appear in this book, and Addison-Wesley was aware of a trademark claim, the designa-
tions have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Weir, Maurice D.
Thomas’ calculus : early transcendentals / Maurice D. Weir, Joel Hass, George B. Thomas.—12th ed.
p. cm
Includes index.
ISBN 978-0-321-58876-0
1. Calculus—Textbooks. 2. Geometry, Analytic—Textbooks. I. Hass, Joel. II. Thomas, George B. (George
Brinton), 1914–2006. III. Title IV. Title: Calculus.
QA303.2.W45 2009
515—dc22 2009023070
Copyright © 2010, 2006, 2001 Pearson Education, Inc. All rights reserved. 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, or otherwise, without the prior written permission of the publisher. Printed in the United
States of America. For information on obtaining permission for use of material in this work, please submit a written
request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA
02116, fax your request to 617-848-7047, or e-mail at http://www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—CRK—12 11 10 09
ISBN-10: 0-321-58876-2
www.pearsoned.com ISBN-13: 978-0-321-58876-0
, CONTENTS
Preface ix
Functions 1
1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 14
1.3 Trigonometric Functions 22
1.4 Graphing with Calculators and Computers 30
1.5 Exponential Functions 34
1.6 Inverse Functions and Logarithms 40
QUESTIONS TO GUIDE YOUR REVIEW 52
PRACTICE EXERCISES 53
ADDITIONAL AND ADVANCED EXERCISES 55
Limits and Continuity 58
2
2.1 Rates of Change and Tangents to Curves 58
2.2 Limit of a Function and Limit Laws 65
2.3 The Precise Definition of a Limit 76
2.4 One-Sided Limits 85
2.5 Continuity 92
2.6 Limits Involving Infinity; Asymptotes of Graphs 103
QUESTIONS TO GUIDE YOUR REVIEW 116
PRACTICE EXERCISES 117
ADDITIONAL AND ADVANCED EXERCISES 119
Differentiation 122
3
3.1 Tangents and the Derivative at a Point 122
3.2 The Derivative as a Function 126
iii
