## Table of Contents

**R. Functions, Graphs, and Models**

R.1 Graphs and Equations

R.2 Functions and Models

R.3 Finding Domain and Range

R.4 Slope and Linear Functions

R.5 Nonlinear Functions and Models

R.6 Mathematical Modeling and Curve Fitting

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application Average Price of a Movie Ticket

**1. Differentiation**

1.1 Limits: A Numerical and Graphical Approach

1.2 Algebraic Limits and Continuity

1.3 Average Rates of Change

1.4 Differentiation Using Limits of Difference Quotients

1.5 The Power and Sum—Difference Rules

1.6 The Product and Quotient Rules

1.7 The Chain Rule

1.8 Higher-Order Derivatives

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–Path of a Baseball: The Tale of the Tape

**2. Applications of Differentiation**

2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs

2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs

2.3 Graph Sketching: Asymptotes and Rational Functions

2.4 Using Derivatives to Find Absolute Maximum and Minimum Values

2.5 Maximum—Minimum Problems; Business, Economics, and General Applications

2.6 Marginals and Differentials

2.7 Elasticity of Demand

2.8 Implicit Differentiation and Related Rates

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–Maximum Sustainable Harvest

**3. Exponential and Logarithmic Functions**

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Applications: Uninhibited and Limited Growth Models

3.4 Applications: Decay

3.5 The Derivatives of a^{x} and log_{a} x

3.6 A Business Application: Amortization

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–The Business of Motion Picture Revenue and DVD Release

**4. Integration**

4.1 Antidifferentiation

4.2 Antiderivatives as Areas

4.3 Area and Definite Integrals

4.4 Properties of Definite Integrals

4.5 Integration Techniques: Substitution

4.6 Integration Techniques: Integration by Parts

4.7 Integration Techniques: Tables

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–Business: Distribution of Wealth

**5. Applications of Integration**

5.1 Consumer Surplus and Producer Surplus

5.2 Integrating Growth and Decay Models

5.3 Improper Integrals

5.4 Probability

5.5 Probability: Expected Value; The Normal Distribution

5.6 Volume

5.7 Differential Equations

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–Curve Fitting and Volumes of Containers

**6. Functions of Several Variables**

6.1 Functions of Several Variables

6.2 Partial Derivatives

6.3 Maximum—Minimum Problems

6.4 An Application: The Least-Squares Technique

6.5 Constrained Optimization

6.6 Double Integrals

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application–Minimizing Employees’ Travel Time in a Building

Cumulative Review

Appendix A: Review of Basic Algebra

Appendix B: Regression and Microsoft Excel

Table A: Areas for a Standard Normal Distribution

Answers

Index of Applications

Index

Additional Instructor’s Answers

**Calculus and Its Applications: Expanded Version (ISBN: 978-0-321-83820-9) contains these additional chapters:**

7. Trigonometric Functions

8. Differential Equations

9. Sequences and Series

10. Probability Distributions