Calculus with Applications

838 Pages·2011·19.936 MB·English

by  Margaret Lial, Ray Greenwell, Nathan Ritchey

This page intentionally left blank
Calculus with Applications
TENTH EDITION
This page intentionally left blank
Calculus with Applications
TENTH EDITION
Margaret L. Lial
American River College
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Youngstown State University
Editor in Chief: Deirdre Lynch
Executive Editor: Jennifer Crum NOTICE:
Executive Content Editor: Christine O’Brien This work is
Senior Project Editor: Rachel S. Reeve protected by U.S.
Editorial Assistant: Joanne Wendelken
copyright laws and
Senior Managing Editor: Karen Wernholm
is provided solely for
Senior Production Project Manager: Patty Bergin
the use of college
Associate Director of Design, USHE North and West: Andrea Nix
Senior Designer: Heather Scott instructors in review-
Digital Assets Manager: Marianne Groth ing course materials
Media Producer: Jean Choe for classroom use.
Software Development: Mary Durnwald and Bob Carroll Dissemination or sale
Executive Marketing Manager: Jeff Weidenaar
of this work,or any
Marketing Coordinator: Caitlin Crain
part (including on the
Senior Author Support/Technology Specialist: Joe Vetere
Rights and Permissions Advisor: Michael Joyce World Wide Web),
Image Manager: Rachel Youdelman will destroy the
Senior Manufacturing Buyer: Carol Melville integrity of the work
Senior Media Buyer: Ginny Michaud and is not permitted.
Production Coordination and Composition: Nesbitt Graphics, Inc.
The work and materi-
Illustrations: Nesbitt Graphics, Inc. and IllustraTech
als from it should
Cover Design: Heather Scott
never be made avail-
Cover Image: Lightpoet/Shutterstock
able to students
Credits appear on page C-1, which constitutes a continuation of the copyright page. except by instructors
using the accompany-
Many of the designations used by manufacturers and sellers to distinguish their products are
ing text in their
claimed as trademarks. Where those designations appear in this book, and Pearson was aware of
classes. All recipi-
a trademark claim, the designations have been printed in initial caps or all caps.
ents of this work are
Library of Congress Cataloging-in-Publication Data expected to abide by
Lial, Margaret L. these restrictions
Calculus with applications — 10th ed. / Margaret L. Lial, Raymond N. and to honor the
Greenwell, Nathan P. Ritchey.
intended pedagogical
p.cm.
purposes and the
Includes bibliographical references and index.
needs of other
ISBN-13: 978-0-321-74900-0 (student ed.)
ISBN-10: 0-321-74900-6 (student ed.) instructors who rely
1. Calculus—Textbooks. I. Greenwell, Raymond N. II. Ritchey, Nathan P. III. Title. on these materials.
QA303.2.L53 2012
515—dc22
2010030933
Copyright ©2012, 2008, 2005, 2002 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, MA02116, fax your request to 617-671-3447, or e-mail at
http://www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—QG—15 14 13 12 11
ISBN-10: 0-321-74900-6
www.pearsonhighered.com ISBN-13: 978-0-321-74900-0
Contents
Preface ix
Dear Student xxi
Prerequisite Skills Diagnostic Test xxii
CHAPTER Algebra Reference R-1
R
R.1 Polynomials R-2
R.2 Factoring R-5
R.3 Rational Expressions R-8
R.4 Equations R-11
R.5 Inequalities R-16
R.6 Exponents R-21
R.7 Radicals R-25
CHAPTER Linear Functions 1
1
1.1 Slopes and Equations of Lines 2
1.2 Linear Functions and Applications 17
1.3 The Least Squares Line 25
CHAPTER 1 REVIEW 38
EXTENDED APPLICATION Using Extrapolation to Predict Life Expectancy 42
CHAPTER Nonlinear Functions 44
2
2.1 Properties of Functions 45
2.2 Quadratic Functions;Translation and Reflection 57
2.3 Polynomial and Rational Functions 67
2.4 Exponential Functions 79
2.5 Logarithmic Functions 89
2.6 Applications:Growth and Decay;Mathematics of Finance 102
CHAPTER 2 REVIEW 110
EXTENDED APPLICATION Power Functions 118
CHAPTER The Derivative 121
3
3.1 Limits 122
3.2 Continuity 140
3.3 Rates of Change 149
3.4 Definition of the Derivative 162
3.5 Graphical Differentiation 180
CHAPTER 3 REVIEW 186
EXTENDED APPLICATION A Model for Drugs Administered Intravenously 193
v
vi CONTENTS
CHAPTER Calculating the Derivative 196
4
4.1 Techniques for Finding Derivatives 197
4.2 Derivatives of Products and Quotients 211
4.3 The Chain Rule 218
4.4 Derivatives of Exponential Functions 228
4.5 Derivatives of Logarithmic Functions 236
CHAPTER 4 REVIEW 243
EXTENDED APPLICATION Electric Potential and Electric Field 248
CHAPTER Graphs and the Derivative 251
5
5.1 Increasing and Decreasing Functions 252
5.2 Relative Extrema 263
5.3 Higher Derivatives,Concavity,and the Second Derivative Test 274
5.4 Curve Sketching 287
CHAPTER 5 REVIEW 296
EXTENDED APPLICATION A Drug Concentration Model for
Orally Administered Medications 300
CHAPTER Applications of the Derivative 303
6
6.1 Absolute Extrema 304
6.2 Applications of Extrema 313
6.3 Further Business Applications:Economic Lot Size;Economic Order Quantity;
Elasticity of Demand 322
6.4 Implicit Differentiation 331
6.5 Related Rates 336
6.6 Differentials:Linear Approximation 343
CHAPTER 6 REVIEW 349
EXTENDED APPLICATION A Total Cost Model for a Training Program 353
CHAPTER Integration 355
7
7.1 Antiderivatives 356
7.2 Substitution 368
7.3 Area and the Definite Integral 376
7.4 The Fundamental Theorem of Calculus 388
7.5 The Area Between Two Curves 398
7.6 Numerical Integration 408
CHAPTER 7 REVIEW 416
EXTENDED APPLICATION Estimating Depletion Dates for Minerals 421
CONTENTS vii
CHAPTER Further Techniques and Applications of Integration 425
8
8.1 Integration by Parts 426
8.2 Volume and Average Value 434
8.3 Continuous Money Flow 441
8.4 Improper Integrals 448
CHAPTER 8 REVIEW 454
EXTENDED APPLICATION Estimating Learning Curves in
Manufacturing with Integrals 457
CHAPTER Multivariable Calculus 459
9
9.1 Functions of Several Variables 460
9.2 Partial Derivatives 471
9.3 Maxima and Minima 482
9.4 Lagrange Multipliers 491
9.5 Total Differentials and Approximations 499
9.6 Double Integrals 504
CHAPTER 9 REVIEW 515
EXTENDED APPLICATION Using Multivariable Fitting to Create a
Response Surface Design 521
CHAPTER Differential Equations 525
10
10.1 Solutions of Elementary and Separable Differential Equations 526
10.2 Linear First-Order Differential Equations 539
10.3 Euler’s Method 545
10.4 Applications of Differential Equations 551
CHAPTER 10 REVIEW 559
EXTENDED APPLICATION Pollution of the Great Lakes 564
CHAPTER Probability and Calculus 567
11
11.1 Continuous Probability Models 568
11.2 Expected Value and Variance of Continuous Random Variables 579
11.3 Special Probability Density Functions 588
CHAPTER 11 REVIEW 600
EXTENDED APPLICATION Exponential Waiting Times 605
viii CONTENTS
CHAPTER Sequences and Series 608
12
12.1 Geometric Sequences 609
12.2 Annuities:An Application of Sequences 613
12.3 Taylor Polynomials at 0 624
12.4 Infinite Series 633
12.5 Taylor Series 639
12.6 Newton’s Method 649
12.7 l’Hôpital’s Rule 653
CHAPTER 12 REVIEW 660
EXTENDED APPLICATION Living Assistance and Subsidized Housing 663
CHAPTER The Trigonometric Functions 665
13
13.1 Definitions of the Trigonometric Functions 666
13.2 Derivatives ofTrigonometric Functions 682
13.3 Integrals ofTrigonometric Functions 692
CHAPTER 13 REVIEW 699
EXTENDED APPLICATION The ShortestTime and the Cheapest Path 704
Appendix
A Solutions to Prerequisite Skills Diagnostic Test A-1
B Learning Objectives A-4
C MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition A-8
D Tables A-10
1 Formulas of Geometry
2 Area Under a Normal Curve
3 Integrals
4 Integrals Involving Trigonometric Functions
Answers to Selected Exercises A-15
Credits C-1
Index of Applications I-1
Index I-5
Sources S-1