Finite Mathematics and Applied Calculus This page intentionally left blank Finite Mathematics and Applied Calculus Fifth Edition Stefan Waner Hofstra University Steven R. Costenoble Hofstra University Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Finite Mathematics and Applied © 2011, 2007Brooks/Cole, Cengage Learning Calculus, Fifth Edition ALL RIGHTS RESERVED. No part of this work covered by the Stefan Waner, Steven R. 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Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09 BRIEF CONTENTS 0 Precalculus Review 1 CHAPTER 1 Functions and Linear Models 39 CHAPTER 2 Systems of Linear Equations and Matrices 123 CHAPTER 3 Matrix Algebra and Applications 181 CHAPTER 4 Linear Programming 263 CHAPTER 5 The Mathematics of Finance 347 CHAPTER 6 Sets and Counting 395 CHAPTER 7 Probability 445 CHAPTER 8 Random Variables and Statistics 547 CHAPTER 9 Nonlinear Functions and Models 619 CHAPTER 10 Introduction to the Derivative 687 CHAPTER 11 Techniques of Differentiation with Applications 781 CHAPTER 12 Further Applications of the Derivative 865 CHAPTER 13 The Integral 947 CHAPTER 14 Further Integration Techniques and Applications CHAPTER of the Integral 1013 15 Functions of Several Variables 1079 CHAPTER 16 Trigonometric Models 1145 CHAPTER v This page intentionally left blank CONTENTS 0 Precalculus Review 1 CHAPTER Introduction 0.1 Real Numbers 2 0.2 Exponents and Radicals 7 0.3 Multiplying and Factoring Algebraic Expressions 17 0.4 Rational Expressions 22 0.5 Solving Polynomial Equations 24 0.6 Solving Miscellaneous Equations 30 0.7 The Coordinate Plane 34 1 Functions and Linear Models 39 CHAPTER Introduction 1.1 Functions from the Numerical, Algebraic, and Graphical Viewpoints 40 1.2 Functions and Models 56 1.3 Linear Functions and Models 75 1.4 Linear Regression 94 KEY CONCEPTS 104 REVIEW EXERCISES 104 CASE STUDY Modeling Spending on Internet Advertising 106 TECHNOLOGY GUIDES 110 2 Systems of Linear Equations and Matrices 123 CHAPTER Introduction 2.1 Systems of Two Equations in Two Unknowns 124 2.2 Using Matrices to Solve Systems of Equations 137 2.3 Applications of Systems of Linear Equations 155 KEY CONCEPTS 168 REVIEW EXERCISES 168 CASE STUDY Hybrid Cars—Optimizing the Degree of Hybridization 171 TECHNOLOGY GUIDES 175 vii viii Contents 3 Matrix Algebra and Applications 181 CHAPTER Introduction 3.1 Matrix Addition and Scalar Multiplication 182 3.2 Matrix Multiplication 192 3.3 Matrix Inversion 206 3.4 Game Theory 217 3.5 Input-Output Models 233 KEY CONCEPTS 246 REVIEW EXERCISES 246 CASE STUDY Projecting Market Share 249 TECHNOLOGY GUIDES 254 4 Linear Programming 263 CHAPTER Introduction 4.1 Graphing Linear Inequalities 264 4.2 Solving Linear Programming Problems Graphically 274 4.3 The Simplex Method: Solving Standard Maximization Problems 290 4.4 The Simplex Method: Solving General Linear Programming Problems 307 4.5 The Simplex Method and Duality 320 KEY CONCEPTS 335 REVIEW EXERCISES 335 CASE STUDY The Diet Problem 339 TECHNOLOGY GUIDES 343 5 The Mathematics of Finance 347 CHAPTER Introduction 5.1 Simple Interest 348 5.2 Compound Interest 356 5.3 Annuities, Loans, and Bonds 367 KEY CONCEPTS 380 REVIEW EXERCISES 380 CASE STUDY Adjustable Rate and Subprime Mortgages 382 TECHNOLOGY GUIDES 388 6 Sets and Counting 395 CHAPTER Introduction 6.1 Sets and Set Operations 396 6.2 Cardinality 407 Contents ix 6.3 The Addition and Multiplication Principles 418 6.4 Permutations and Combinations 428 KEY CONCEPTS 441 REVIEW EXERCISES 441 CASE STUDY Designing a Puzzle 443 7 Probability 445 CHAPTER Introduction 7.1 Sample Spaces and Events 446 7.2 Relative Frequency 460 7.3 Probability and Probability Models 468 7.4 Probability and Counting Techniques 487 7.5 Conditional Probability and Independence 495 7.6 Bayes’Theorem and Applications 512 7.7 Markov Systems 521 KEY CONCEPTS 536 REVIEW EXERCISES 536 CASE STUDY The Monty Hall Problem 539 TECHNOLOGY GUIDES 541 8 Random Variables and Statistics 547 CHAPTER Introduction 8.1 Random Variables and Distributions 548 8.2 Bernoulli Trials and Binomial Random Variables 559 8.3 Measures of Central Tendency 567 8.4 Measures of Dispersion 580 8.5 Normal Distributions 594 KEY CONCEPTS 606 REVIEW EXERCISES 606 CASE STUDY Spotting Tax Fraud with Benford’s Law 608 TECHNOLOGY GUIDES 612 9 Nonlinear Functions and Models 619 CHAPTER Introduction 9.1 Quadratic Functions and Models 620 9.2 Exponential Functions and Models 632 9.3 Logarithmic Functions and Models 647