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Marvin L. Bittinger Indiana University Purdue University Indianapolis

David J. Ellenbogen Community College of Vermont

Scott A. Surgent Arizona State University

10 Calculus and its applications

EDITION

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Library of Congress Cataloging-in-Publication Data Bittinger, Marvin L. Calculus and its applications. — 10th ed./Marvin L. Bittinger,

David J. Ellenbogen, Scott A. Surgent. p. cm.

Includes index. 1. Calculus—Textbooks. I. Ellenbogen, David. II. Surgent, Scott A. III. Title. QA303.2.B466 2012 515—dc22 2010017892

Copyright © 2012 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 permis- sion of the publisher. Printed in the United States of America. For information on obtaining per- mission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Boston, MA, 02116.

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ISBN-10: 0-321-69433-3 ISBN-13: 978-0-321-69433-1

N O T I C E : This work is

protected by U.S. copyright laws and is provided solely for the use of college instructors in review- ing course materials for classroom use. Dissemination or sale of this work, or any part (including on the World Wide Web), will destroy the integrity of the work and is not permitted. The work and materi- als from it should never be made avail- able to students except by instructors using the accompany- ing text in their classes. All recipi- ents of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

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To: Elaine, Victoria, and Beth

Contents Preface vii Prerequisite Skills Diagnostic Test xix

CHAPTER R

Functions, Graphs, and Models 1 R.1 Graphs and Equations 2 R.2 Functions and Models 13 R.3 Finding Domain and Range 24 R.4 Slope and Linear Functions 33 R.5 Nonlinear Functions and Models 50 R.6 Mathematical Modeling and Curve Fitting 68 Chapter Summary 79 Chapter Review Exercises 85 Chapter Test 88 Extended Technology Application

Average Price of a Movie Ticket 90

CHAPTER 1

Differentiation 93 1.1 Limits: A Numerical and Graphical

Approach 94 1.2 Algebraic Limits and Continuity 109 1.3 Average Rates of Change 121 1.4 Differentiation Using Limits

of Difference Quotients 132 1.5 Differentiation Techniques: The Power

and Sum–Difference Rules 144 1.6 Differentiation Techniques: The Product

and Quotient Rules 158 1.7 The Chain Rule 166 1.8 Higher-Order Derivatives 177 Chapter Summary 185 Chapter Review Exercises 190 Chapter Test 192 Extended Technology Application

Path of a Baseball:The Tale of the Tape 194

iv

CHAPTER 2

Applications of Differentiation 197 2.1 Using First Derivatives to Find Maximum

and Minimum Values and Sketch Graphs 198 2.2 Using Second Derivatives to Find Maximum

and Minimum Values and Sketch Graphs 216 2.3 Graph Sketching: Asymptotes and Rational

Functions 234 2.4 Using Derivatives to Find Absolute Maximum

and Minimum Values 250 2.5 Maximum–Minimum Problems;

Business and Economics Applications 262 2.6 Marginals and Differentials 277 2.7 Implicit Differentiation and Related Rates 288 Chapter Summary 295 Chapter Review Exercises 301 Chapter Test 303 Extended Technology Application

Maximum Sustainable Harvest 305

CHAPTER 3

Exponential and Logarithmic Functions 307 3.1 Exponential Functions 308 3.2 Logarithmic Functions 322 3.3 Applications: Uninhibited and Limited

Growth Models 337 3.4 Applications: Decay 353 3.5 The Derivatives of ax and loga x 366 3.6 An Economics Application:

Elasticity of Demand 371 Chapter Summary 378 Chapter Review Exercises 382 Chapter Test 384 Extended Technology Application

The Business of Motion Picture Revenue and DVD Release 385

C O N T E N T S v

Cumulative Review 602 Appendix A: Review of Basic Algebra 605 Appendix B: Regression and

Microsoft Excel 616 Appendix C: MathPrint Operating

System for TI-84 and TI-84 Plus Silver Edition 618

Table A: Areas for a Standard Normal Distribution 621

Answers A-1 Index of Applications I-1 Index I-4

CHAPTER 4

Integration 389 4.1 Antidifferentiation 390 4.2 Antiderivatives as Areas 399 4.3 Area and Definite Integrals 410 4.4 Properties of Definite Integrals 425 4.5 Integration Techniques: Substitution 436 4.6 Integration Techniques:

Integration by Parts 445 4.7 Integration Techniques: Tables 454 Chapter Summary 459 Chapter Review Exercises 466 Chapter Test 468 Extended Technology Application

Business: Distribution of Wealth 469

CHAPTER 5

Applications of Integration 473 5.1 An Economics Application:

Consumer Surplus and Producer Surplus 474 5.2 Applications of Integrating Growth

and Decay Models 480 5.3 Improper Integrals 492 5.4 Probability 498 5.5 Probability: Expected Value;

The Normal Distribution 508 5.6 Volume 522 5.7 Differential Equations 526 Chapter Summary 535 Chapter Review Exercises 541 Chapter Test 543 Extended Technology Application

Curve Fitting and Volumes of Containers 545

CHAPTER 6

Functions of Several Variables 547 6.1 Functions of Several Variables 548 6.2 Partial Derivatives 556 6.3 Maximum–Minimum Problems 565 6.4 An Application:

The Least-Squares Technique 572 6.5 Constrained Optimization 579 6.6 Double Integrals 588 Chapter Summary 594 Chapter Review Exercises 598 Chapter Test 599 Extended Technology Application

Minimizing Employees’ Travel Time in a Building 600

SUPPLEMENTARY CHAPTERS Available to qualified instructors through the Pearson Instructor Resource Center (www.pearsonhighered.com/ irc) and to students at the downloadable student resources site (www.pearsonhighered.com/mathstatsresources) or within MyMathLab

A. Sequences and Series online A.1 Infinite Sequences A.2 Infinite Series A.3 The Ratio Test and Power Series A.4 Taylor Series and Taylor Polynomials Summary and Review Test

B. Differential Equations online B.1 Further Background B.2 First-Order Linear Differential Equations B.3 Graphical Analysis B.4 Numerical Analysis: Euler’s Method Summary and Review Test

C. Trigonometric Functions online C.1 Introduction to Trigonometry C.2 Derivatives of the Trigonometric Functions C.3 Integration of the Trigonometric Functions C.4 Inverse Trigonometric Functions Summary and Review Test

www.pearsonhighered.com/irc www.pearsonhighered.com/irc www.pearsonhighered.com/mathstatsresources

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