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CONTENTS

CHAPTER 1 PRELIMINARIES

1.1 Precalculus Review I 11.2 Precalculus Review II 121.3 The Cartesian Coordinate System 221.4 Straight Lines 29

Chapter 1 Review Exercises 42

CHAPTER 2 FUNCTIONS, LIMITS, AND THE DERIVATIVE

2.1 Functions and Their Graphs 522.2 The Algebra of Functions 77

2.3 Functions and Mathematical Models 862.4 Limits 1062.5 One-Sided Limits and Continuity 1202.6 The Derivative 132

Chapter 2 Review Exercises 152

CHAPTER 3 DIFFERENTIATION

3.1 Basic Rules of Differentiation 1683.2 The Product and Quotient Rules 1803.3 The Chain Rule 1963.4 Marginal Functions in Economics 212

3.5 Higher-Order Derivatives 2223.6 Implicit Differentiation and Related Rates 2303.7 Differentials 246

Chapter 3 Review Exercises 255

CHAPTER 4 APPLICATIONS OF THE DERIVATIVE

4.1 Applications of the First Derivative 2704.2 Applications of the Second Derivative 2944.3 Curve Sketching 3134.4 Optimization I 3484.5 Optimization II 370

Chapter 4 Review Exercises 382

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CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

5.1 Exponential Functions 4095.2 Logarithmic Functions 4185.3 Compound Interest 4255.4 Differentiation of Exponential Functions 4335.5 Differentiation of Logarithmic Functions 4515.6 Exponential Functions as Mathematical Models 463

Chapter 5 Review Exercises 475

CHAPTER 6 INTEGRATION

6.1 Antiderivatives and the Rules of Integration 4876.2 Integration by Substitution 4996.3 Area and the Definite Integral 5126.4 The Fundamental Theorem of Calculus 5176.5 Evaluating Definite Integrals 5246.6 Area Between Two Curves 5346.7 Applications of the Definite Integral to Business and Economics 5486.8 Volumes of Solids of Revolution 553

Chapter 6 Review Exercises 559

CHAPTER 7 ADDITIONAL TOPICS IN INTEGRATION

7.1 Integration by Parts 5757.2 Integration Using Tables of Integrals 5867.3 Numerical Integration 5957.4 Improper Integrals 608

Chapter 7 Review Exercises 615

CHAPTER 8 CALCULUS OF SEVERAL VARIABLES

8.1 Functions of Several Variables 6258.2 Partial Derivatives 6318.3 Maxima and Minima of Functions of Several Variables 6408.4 The Method of Least Squares 6528.5 Constrained Maxima and Minima and the Method of

Lagrange Multipliers 6678.6 Total Differentials 6798.7 Double Integrals 686

8.8 Applications of Double Integrals 690Chapter 8 Review Exercises 696

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CHAPTER 9 DIFFERENTIAL EQUATIONS

9.1 Differential Equations 7129.2 Separation of Variables 7199.3 Applications of Separable Differential Equations 7279.4 Approximate Solutions of Differential Equations 734

Chapter 9 Review Exercises 744

CHAPTER 10 PROBABILITY AND CALCULUS

10.1 Probability Distributions of Random Variables 75610.2 Expected Value and Standard Deviation 76810.3 Normal Distributions 776

Chapter 10 Review Exercises 782

CHAPTER 11 TAYLOR POLYNOMIALS AND INFINITE SERIES

11.1 Taylor Polynomials 78811.2 Infinite Sequences 80111.3 Infinite Series 80711.4 Series with Positive Terms 81511.5 Power Series and Taylor Series 82711.6 More on Taylor Series 83411.7 The Newton-Raphson Method 843

Chapter 11 Review Exercises 853

CHAPTER 12 TRIGONOMETRIC FUNCTIONS

12.1 Measurement of Angles 86612.2 The Trigonometric Functions 86912.3 Differentiation of Trigonometric Functions 87412.4 Integration of Trigonometric Functions 887

Chapter 12 Review Exercises 898