net This page intentionally left blank www.net Finite Mathematics and Calculus with Applications NINTH EDITION Margaret L. Lial American River College Raymond N. Greenwell Hofstra University Nathan P. Ritchey Youngstown State University www.net 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. Editorial Assistant: Joanne Wendelken copyright laws and Senior Managing Editor: Karen Wernholm Senior Production Project Manager: Patty Bergin is provided solely for Associate Director of Design, USHE North and West: Andrea Nix the use of college 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 Marketing Coordinator: Caitlin Crain of this work, or any Senior Author Support/Technology Specialist: Joe Vetere part (including on the Rights and Permissions Advisor: Michael Joyce World Wide Web), will Image Manager: Rachel Youdelman destroy the integrity Senior Manufacturing Buyer: Carol Melville of the work and is Senior Media Buyer: Ginny Michaud not permitted. The Production Coordination and Composition: Nesbitt Graphics, Inc.
Illustrations: Nesbitt Graphics, Inc. and IllustraTech work and materials Cover Design: Heather Scott from it should never Cover Image: John Wollwerth/Shutterstock be made available to students except by Credits appear on page C-1, which constitutes a continuation of the copyright page. instructors using the accompanying text in 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 Pearson was aware of their classes.
All a trademark claim, the designations have been printed in initial caps or all caps. recipients of this work are expected to Library of Congress Cataloging-in-Publication Data abide by these Lial, Margaret L. restrictions and to Finite mathematics and calculus with applications. — 9th honor the intended ed.
pedagogical purposes Ritchey. and the needs of Includes bibliographical references and index. other instructors who ISBN-13: 978-0-321-74908-6 rely on these materi- ISBN-10: 0-321-74908-1 als.L54 2013 510 — dc22 2010031432 Copyright © 2012, 2009, 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, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.com/legal/permissions. 1 2 3 4 5 6 7 8 9 10—QG—15 14 13 12 11 ISBN-10: 0-321-74908-1 www.com ISBN-13: 978-0-321-74908-6 www.net Contents Preface ix Dear Student xxii Prerequisite Skills Diagnostic Test xxiii CHAPTER Algebra Reference R-1 R R.7 Radicals R-25 CHAPTER Linear Functions 1 1 1.2 Slopes and Equations of Lines Linear Functions and Applications 2 17 1.3 The Least Squares Line 25 CHAPTER 1 REVIEW 38 EXTENDED APPLICATION Using Extrapolation to Predict Life Expectancy 42 CHAPTER Systems of Linear Equations and Matrices 44 2 2.2 Solution of Linear Systems by the Echelon Method Solution of Linear Systems by the Gauss-Jordan Method 45 54 2.3 Addition and Subtraction of Matrices 70 2.4 Multiplication of Matrices 77 2.6 Input-Output Models 97 CHAPTER 2 REVIEW 104 EXTENDED APPLICATION Contagion 110 CHAPTER Linear Programming:The Graphical Method 112 3 3.2 Graphing Linear Inequalities 113 Solving Linear Programming Problems Graphically 120 3.3 Applications of Linear Programming 126 CHAPTER 3 REVIEW 134 EXTENDED APPLICATION Sensitivity Analysis 137 iii www.net iv CONTENTS CHAPTER Linear Programming:The Simplex Method 142 4 4.2 Slack Variables and the Pivot Maximization Problems 150 143 4.3 Minimization Problems; Duality 161 4.4 Nonstandard Problems 170 CHAPTER 4 REVIEW 179 EXTENDED APPLICATION Using Integer Programming in the Stock-Cutting Problem 183 CHAPTER Mathematics of Finance 187 5 5.2 Simple and Compound Interest Future Value of an Annuity 200 188 5.3 Present Value of an Annuity; Amortization 209 CHAPTER 5 REVIEW 218 EXTENDED APPLICATION Time, Money, and Polynomials 222 CHAPTER Logic 224 6 6.2 Statements 225 Truth Tables and Equivalent Statements 233 6.3 The Conditional and Circuits 240 6.4 More on the Conditional 250 6.5 Analyzing Arguments and Proofs 257 6.6 Analyzing Arguments with Quantifiers 266 CHAPTER 6 REVIEW 274 EXTENDED APPLICATION Logic Puzzles 279 CHAPTER Sets and Probability 283 7 7.2 Sets 284 Applications of Venn Diagrams 292 7.3 Introduction to Probability 302 7.4 Basic Concepts of Probability 311 7.5 Conditional Probability; Independent Events 322 7.6 Bayes’ Theorem 336 CHAPTER 7 REVIEW 343 EXTENDED APPLICATION Medical Diagnosis 350 www.net CONTENTS v CHAPTER Counting Principles; Further Probability Topics 352 8 8.2 The Multiplication Principle; Permutations Combinations 361 353 8.3 Probability Applications of Counting Principles 370 8.5 Probability Distributions; Expected Value 389 CHAPTER 8 REVIEW 400 EXTENDED APPLICATION Optimal Inventory for a Service Truck 405 CHAPTER Statistics 407 9 9.2 Frequency Distributions; Measures of Central Tendency Measures of Variation 419 408 9.3 The Normal Distribution 428 9.4 Normal Approximation to the Binomial Distribution 438 CHAPTER 9 REVIEW 445 EXTENDED APPLICATION Statistics in the Law—The Castaneda Decision 449 CHAPTER Nonlinear Functions 452 10 10.1 Properties of Functions 453 10.2 Quadratic Functions;Translation and Reflection 465 10.3 Polynomial and Rational Functions 475 10.6 Applications: Growth and Decay; Mathematics of Finance 510 CHAPTER 10 REVIEW 518 EXTENDED APPLICATION Power Functions 526 CHAPTER The Derivative 529 11 11.3 Rates of Change 557 11.4 Definition of the Derivative 570 11.5 Graphical Differentiation 588 CHAPTER 11 REVIEW 594 EXTENDED APPLICATION A Model for Drugs Administered Intravenously 601 www.net vi CONTENTS CHAPTER Calculating the Derivative 604 12 12.1 Techniques for Finding Derivatives 12.2 Derivatives of Products and Quotients 605 619 12.3 The Chain Rule 626 12.4 Derivatives of Exponential Functions 636 12.5 Derivatives of Logarithmic Functions 644 CHAPTER 12 REVIEW 651 EXTENDED APPLICATION Electric Potential and Electric Field 656 CHAPTER Graphs and the Derivative 659 13 13.1 Increasing and Decreasing Functions 13.3 Higher Derivatives, Concavity, and the Second Derivative Test 682 13.4 Curve Sketching 695 CHAPTER 13 REVIEW 704 EXTENDED APPLICATION A Drug Concentration Model for Orally Administered Medications 708 CHAPTER Applications of the Derivative 711 14 14.2 Applications of Extrema 712 721 14.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand 730 14.6 Differentials: Linear Approximation 751 CHAPTER 14 REVIEW 757 EXTENDED APPLICATION A Total Cost Model for a Training Program 761 CHAPTER Integration 763 15 15.3 Area and the Definite Integral 784 15.4 The Fundamental Theorem of Calculus 796 15.5 The Area Between Two Curves 806 15.6 Numerical Integration 816 CHAPTER 15 REVIEW 824 EXTENDED APPLICATION Estimating Depletion Dates for Minerals 829 www.net CONTENTS vii CHAPTER Further Techniques and Applications of Integration 833 16 16.1 Integration by Parts 16.2 Volume and Average Value 834 842 16.3 Continuous Money Flow 849 16.5 Solution of Elementary and Separable Differential Equations 862 CHAPTER 16 REVIEW 875 EXTENDED APPLICATION Estimating Learning Curves in Manufacturing with Integrals 880 CHAPTER Multivariable Calculus 883 17 17.1 Functions of Several Variables 17.3 Maxima and Minima 906 17.5 Total Differentials and Approximations 923 17.6 Double Integrals 928 CHAPTER 17 REVIEW 939 EXTENDED APPLICATION Using Multivariable Fitting to Create a Response Surface Design 945 CHAPTER Probability and Calculus 949 18 18.1 Continuous Probability Models 950 18.2 Expected Value and Variance of Continuous Random Variables 961 18.3 Special Probability Density Functions 970 CHAPTER 18 REVIEW 982 EXTENDED APPLICATION Exponential Waiting Times 987 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-10 D Tables A-12 1 Formulas from Geometry 2 Area Under a Normal Curve 3 Integrals www.net viii CONTENTS Answers to Selected Exercises A-17 Credits C-1 Index of Applications I-1 Index I-7 Sources S-1 Special Topics to Accompany Finite Mathematics and Calculus with Applications The following material is provided free to adopters at www.com/mathstatsresources: Digraphs and Networks Graphs and Digraphs Dominance Digraphs Communication Digraphs Networks Review Exercises www.net Preface Finite Mathematics and Calculus with Applications is a thorough, application-oriented text for students majoring in business, management, economics, or the life or social sciences.
In addition to its clear exposition, this text consistently connects the mathematics to career and everyday-life situations. A prerequisite of two years of high school algebra is assumed. A renewed focus on quick and effective assessments, new applications and exercises, as well as other new learning tools make this 9th edition an even richer learning resource for students. Our Approach Our main goal is to present finite mathematics and applied calculus in a concise and meaningful way so that students can understand the full picture of the concepts they are learning and apply it to real-life situations.
This is done through a variety of ways. Focus on Applications Making this course meaningful to students is critical to their success. Applications of the mathematics are integrated throughout the text in the exposition, the examples, the exercise sets, and the supplementary resources. Finite Mathematics and Calculus with Applications presents students with a myriad of opportunities to relate what they’re learning to career situations through the Apply It questions, the applied examples, and the Extended Applications.
To get a sense of the breadth of applications presented, look at the Index of Applications in the back of the book or the extended list of sources of real-world data on www. Pedagogy to Support Students Students need careful explanations of the mathematics along with examples presented in a clear and consistent manner. Additionally students and instructors should have a means to assess the basic prerequisite skills. This can now be done with the Prerequisite Skills Diagnostic Test located just before Chapter R.
In addition, the stu- dents need a mechanism to check their understanding as they go and resources to help them remediate if necessary. Finite Mathematics and Calculus with Applications has this support built into the pedagogy of the text through fully developed and annotated examples, Your Turn exercises, For Review references, and supplementary material. Beyond the Textbook Students today take advantage of a variety of resources and delivery methods for instruction. As such, we have developed a robust MyMathLab course for Finite Mathematics and Calculus with Applications.
MyMathLab has a well-established and well- documented track record of helping students succeed in mathematics. The MyMathLab online course for Finite Mathematics and Calculus with Applications contains over 6700 exer- cises to challenge students and provides help when they need it. Students who learn best by seeing and hearing can view section- and example-level videos within MyMathLab or on the book-specific DVD-Rom. These and other resources are available to students as a unified and reliable tool for their success.
New to the Ninth Edition Based on the authors’ experience in the classroom along with feedback from many instructors across the country, the focus of this revision is to improve the clarity of the presentation and provide students with more opportunities to learn, practice, and apply what they’ve learned on their own. This is done in both the presentation of the content and in new features added to the text.net x PREFACE New and Revised Content • Chapter R The flow of the material was improved by reordering some exercises and examples. Exercises were added to Section R. • Chapter 1 Changes in the presentation were made throughout to increase clarity, includ- ing adding some examples and rewriting others.
Terminology in Section 1.2 was adjusted to be more consistent with usage in economics.1 was changed so that only systems of two equations are solved by the echelon method, while systems with three or more equations are solved using the Gauss-Jordan method in Section 2. The discussion of subtraction of matrices in Section 2.3 was simplified. • Chapter 3 The concept of bounded and unbounded regions was moved from Section 3.1, where such regions are first encountered. An Extended Application on sensi- tivity analysis was added to this chapter.