## Table of Contents

Preface.

1. PRELIMINARIES.

Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines. Chapter 1 Summary of Principal Formulas and Terms. Chapter 1 Concept Review Questions. Chapter 1 Review Exercises. Chapter 1 Before Moving On.

2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.

Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Portfolio. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Chapter 2 Summary of Principal Formulas and Terms. Chapter 2 Concept Review Questions. Chapter 2 Review Exercises. Chapter 2 Before Moving On.

3. DIFFERENTIATION.

Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Using Technology: Finding the Differential of a Function. Chapter 3 Summary of Principal Formulas and Terms. Chapter 3 Concept Review Questions. Chapter 3 Review Exercises. Chapter 3 Before Moving On.

4. APPLICATIONS OF THE DERIVATIVE.

Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Chapter 4 Summary of Principal Terms. Chapter 4 Concept Review Questions. Chapter 4 Review Exercises. Chapter 4 Before Moving On.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions. Using Technology. Logarithmic Functions. Compound Interest. Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment. Differentiation of Exponential Functions. Using Technology. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Portfolio. Using Technology: Analyzing Mathematical Models. Chapter 5 Summary of Principal Formulas and Terms. Chapter 5 Concept Review Questions. Chapter 5 Review Exercises. Chapter 5 Before Moving On.

6. INTEGRATION.

Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Portfolio. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Business and Economic Applications/Technology Exercises. Chapter 6 Summary of Principal Formulas and Terms. Chapter 6 Concept Review Questions. Chapter 6 Review Exercises. Chapter 6 Before Moving On.

7. ADDITIONAL TOPICS IN INTEGRATION.

Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Calculus to Probability. Chapter 7 Summary of Principal Formulas and Terms. Chapter 7 Concept Review Questions. Chapter 7 Review Exercises. Chapter 7 Before Moving On.

8. CALCULUS OF SEVERAL VARIABLES.

Functions of Several Variables. Partial Derivatives. Portfolio. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Chapter 8 Summary of Principal Formulas and Terms. Chapter 8 Concept Review Questions. Chapter 8 Review Exercises. Chapter 8 Before Moving On.

Appendix A.

The Inverse of a Function. The Graphs of Inverse Functions. Functions That Have Inverses. Finding the Inverse of a Function.

Appendix B.

Indeterminant Forms and l'Hôpital's Rule. The Indeterminant Forms 0/0 and ∞/ ∞.

Index.

## Supplements

## Instructor Supplements

# Instructor Supplements

All supplements have been updated in coordination with the main title. Select the main title’s "About the Solution" tab, then select "What's New" for updates specific to title's edition.
**For more information about these supplements, or to obtain them, contact your Learning Consultant.**

###
Mathematics CourseMate with eBook Instant Access Code
(ISBN-10: 1111765553 | ISBN-13: 9781111765552)

Interested in a simple way to complement your text and course content with study and practice materials? Cengage Learning’s CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Watch student comprehension soar as your class works with the printed textbook and the textbook-specific website. CourseMate goes beyond the book to deliver what you need!

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PowerLecture
(ISBN-10: 0840035225 | ISBN-13: 9780840035226)

This CD-ROM provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM.

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ExamView®
(ISBN-10: 1111426554 | ISBN-13: 9781111426552)

Available on the PowerLecture™ CD and featuring automatic grading, ExamView® testing software allows instructors to quickly create, deliver, and customize tests for class in print and online formats. The program includes a test bank with hundreds of questions customized directly to the text, with all questions also provided in PDF and Microsoft® Word formats for instructors who opt not to use the software component.

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Enhanced WebAssign - Start Smart Guide for Students
(ISBN-10: 0495384798 | ISBN-13: 9780495384793)

This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.

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Student Solutions Manual
(ISBN-10: 0840068476 | ISBN-13: 9780840068477)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

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Enhanced WebAssign Single-Term LOE Instant Access for Applied Math
(ISBN-10: 1285857615 | ISBN-13: 9781285857619)

IMPORTANT: When purchasing this instant access code for Applied Math, ensure that you are using it in one of the following courses: Applied Math, Finite Math or Applied Calculus. Use with a different course may cause complications with access.
Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code.
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List Price = $65.00
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## Student Supplements

# Student Supplements

All supplements have been updated in coordination with the main title. Select the main title’s "About the Solution" tab, then select "What's New" for updates specific to title's edition.
**For more information about these supplements, or to obtain them, contact your Learning Consultant.**

###
Mathematics CourseMate with eBook Instant Access Code
(ISBN-10: 1111765553 | ISBN-13: 9781111765552)

The more you study, the better the results. Make the most of your study time by accessing everything you need to succeed in one place. Read your textbook, take notes, review flashcards, watch videos, and take practice quizzes—online with CourseMate.

List Price = $134.00
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| College Bookstore Wholesale Price = $134.00

###
Enhanced WebAssign - Start Smart Guide for Students
(ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = $39.95
| CengageBrain Price = $39.49
| College Bookstore Wholesale Price = $29.75

###
Student Solutions Manual
(ISBN-10: 0840068476 | ISBN-13: 9780840068477)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives you the information you need to truly understand how these problems are solved.

List Price = $82.95
| CengageBrain Price = $82.49
| College Bookstore Wholesale Price = $61.50

###
Enhanced WebAssign Single-Term LOE Instant Access for Applied Math
(ISBN-10: 1285857615 | ISBN-13: 9781285857619)

IMPORTANT: When purchasing this instant access code for Applied Math, ensure that you are using it in one of the following courses: Applied Math, Finite Math or Applied Calculus. Use with a different course may cause complications with access.
Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code.
This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $65.00
| CengageBrain Price = $65.00
| College Bookstore Wholesale Price = $65.00