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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
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
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
Chapter Summary 266
Important Terms, Symbols, and Formulas 266
Checkup for Chapter 3 267
Review Problems 268
Explore! Update 274
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
Chapter Summary 340
Important Terms, Symbols, and Formulas 340
Checkup for Chapter 4 342
Review Problems 343
Explore! Update 349
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
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
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
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
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