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CONTENTS Preface vi C H A P T E R 1 Functions, Graphs, and Limits 1 Functions 2 2 The Graph of a Function 14 3 Linear Functions 26 4 Functional Models 41 5 Limits 57 6 One-Sided Limits and Continuity 71 Chapter Summary 83 Important Terms, Symbols, and Formulas 83 Checkup for Chapter 1 83 Review Problems 84 Explore! Update 89 Think About It 91 C H A P T E R 2 Differentiation: Basic Concepts 1 The Derivative 96 2 Techniques of Differentiation 110 3 Product and Quotient Rules; Higher-Order Derivatives 122 4 The Chain Rule 135 5 Marginal Analysis and Approximations Using Increments 147 6 Implicit Differentiation and Related Rates 158 Chapter Summary 170 Important Terms, Symbols, and Formulas 170 Checkup for Chapter 2 171 Review Problems 172 Explore! Update 178 Think About It 180 C H A P T E R 3 Additional Applications of the Derivative 1 Increasing and Decreasing Functions; Relative Extrema 184 2 Concavity and Points of Inflection 199 3 Curve Sketching 216 4 Optimization 231 5 Additional Applied Optimization 249 Chapter Summary 266 Important Terms, Symbols, and Formulas 266 Checkup for Chapter 3 267 Review Problems 268 Explore! Update 274 Think About It 277 C H A P T E R 4 Exponential and Logarithmic Functions 1 Exponential Functions 282 2 Logarithmic Functions 297 3 Differentiation of Logarithmic and Exponential Functions 312 4 Additional Exponential Models 326 Chapter Summary 340 Important Terms, Symbols, and Formulas 340 Checkup for Chapter 4 342 Review Problems 343 Explore! Update 349 Think About It 351 C H A P T E R 5 Integration 1 Antidifferentiation: The Indefinite Integral 356 2 Integration by Substitution 368 3 The Definite Integral and the Fundamental Theorem of Calculus 380 4 Applying Definite Integration: Area Between Curves and Average Value 396 5 Additional Applications to Business and Economics 414 6 Additional Applications to the Life and Social Sciences 426 Chapter Summary 436 Important Terms, Symbols, and Formulas 436 Checkup for Chapter 5 437 Review Problems 438 Explore! Update 442 Think About It 445 C H A P T E R 6 Additional Topics in Integration 1 Integration by Parts; Integral Tables 450 2 Introduction to Differential Equations 464 3 Improper Integrals; Continuous Probability 480 4 Numerical Integration 496 Chapter Summary 508 Important Terms, Symbols, and Formulas 508 Checkup for Chapter 6 509 Review Problems 510 Explore! Update 516 Think About It 519 C H A P T E R 7 Calculus of Several Variables 1 Functions of Several Variables 526 2 Partial Derivatives 540 3 Optimizing Functions of Two Variables 551 4 The Method of Least-Squares 563 5 Constrained Optimization: The Method of Lagrange Multipliers 575 6 Double Integrals over Rectangular Regions 589 Chapter Summary 599 Important Terms, Symbols, and Formulas 599 Checkup for Chapter 7 600 Review Problems 601 Explore! Update 605 Think About It 607 A P P E N D I X A Algebra Review 1 A Brief Review of Algebra 612 2 Factoring Polynomials and Solving Systems of Equations 622 3 Evaluating Limits with L?Hopital?s Rule 629 Appendix Summary 634 Important Terms, Symbols, and Formulas 634 Review Problems 634 Think About It 637 T A B L E S I Powers of e 639 II The Natural Logarithm (Base e) 640 T E X T S O L U T I O N S Answers to Odd-Numbered Problems, Chapter Checkup Problems, and Chapter Review Problems 641 Index 717

Library of Congress Subject Headings for this publication:

Calculus -- Textbooks.