## Table of Contents

A Preview of Calculus.

1. FUNCTIONS AND LIMITS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Review. Principles of Problem Solving.

2. DERIVATIVES.

Derivatives and Rates of Change. Writing Project: Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Laboratory Project: Families of Implicit Curves. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Problems Plus.

3. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity; Horizontal Asymptotes. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton’s Method. Antiderivatives. Review. Problems Plus.

4. INTEGRALS.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

5. APPLICATIONS OF INTEGRATION.

Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Review. Problems Plus.

6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS

Inverse Functions. (Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4*. See the Preface). Exponential Functions and Their Derivatives. Logarithmic Functions.

Derivatives of Logarithmic Functions. *The Natural Logarithmic Function. *The Natural Exponential Function. *General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Applied Project: Where to Sit at the Movies. Hyperbolic Functions. Indeterminate Forms and l’Hospital’s Rule. Writing Project: The Origins of l’Hospital’s Rule. Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Euler’s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bézier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.

Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

Appendix A: Intervals, Inequalities, and Absolute Values.

Appendix B: Coordinate Geometry and Lines.

Appendix C: Graphs of Second-Degree Equations.

Appendix D: Trigonometry.

Appendix E: Sigma Notation.

Appendix F: Proofs of Theorems.

Appendix G: Graphing Calculators and Computers.

Appendix H: Complex Numbers.

Appendix I: Answers to Odd-Numbered Exercises.

## 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.**

###
Single Variable Calculus, Hybrid Edition
(ISBN-10: 1111426759 | ISBN-13: 9781111426750)

Reflecting Cengage Learning’s commitment to offering flexible teaching solutions and value for students and instructors, these new hybrid versions feature the instructional presentation found in the printed text while delivering end-of-section and/or end-of chapter exercises online in Enhanced WebAssign. The result—a briefer printed text that engages students online! James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of SINGLE VARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence. CourseSmart goes beyond traditional expectations–providing instant, online access to the textbooks and course materials you need and at a lower cost to your students. To request an electronic sample of this Cengage Learning title, go to: www.coursesmart.com/instructors.

List Price = $146.95
| College Bookstore Wholesale Price = $108.50

###
Single Variable Calculus, Volume 1
(ISBN-10: 053849784X | ISBN-13: 9780538497848)

James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of SINGLE VARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

List Price = $172.95
| CengageBrain Price = $137.99
| College Bookstore Wholesale Price = $127.75

###
Single Variable Calculus, Volume 2
(ISBN-10: 0538497858 | ISBN-13: 9780538497855)

James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of SINGLE VARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

List Price = $172.95
| CengageBrain Price = $137.99
| College Bookstore Wholesale Price = $127.75

###
Instructor's Guide
(ISBN-10: 0840054076 | ISBN-13: 9780840054074)

Enrich the way you teach the course with the Instructor's Guide for Stewart's Calculus, 7E. Each section of the main text is discussed from several viewpoints and contains suggested time to allot, points to stress, text discussion topics, core materials for lecture, workshop/discussion suggestions, group work exercises in a form suitable for handout, and suggested homework problems. The guide includes single variable and multivariable content. An electronic version is available on PowerLecture.

###
PowerLecture
(ISBN-10: 0840054149 | ISBN-13: 9780840054142)

Equip yourself with the dynamic teaching tools available with PowerLecture CD-ROM. 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. Enhance your lectures with Microsoft® PowerPoint® lecture slides and figures from the book.

###
Test Bank
(ISBN-10: 0840054084 | ISBN-13: 9780840054081)

Includes multiple-choice and short-answer test items that key directly to the text. (Includes single variable and multivariable content).

###
Complete Solutions Manual (Chapters 1-11)
(ISBN-10: 0840053029 | ISBN-13: 9780840053022)

This manual includes worked-out solutions to every exercise in Single Variable Calculus, 7e (Chapters 1-11 of Calculus, 7e).

###
Student Solutions Manual (Chapters 1-11)
(ISBN-10: 0840049498 | ISBN-13: 9780840049490)

This manual includes worked-out solutions to every odd-numbered exercise in Single Variable Calculus, 7e (Chapters 1-11 of Calculus, 7e).

List Price = $107.95
| CengageBrain Price = $107.49
| College Bookstore Wholesale Price = $79.75

###
Study Guide, SV
(ISBN-10: 0840054092 | ISBN-13: 9780840054098)

For each section of Stewart's Single Variable text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained answers. It also contains "Technology Plus" questions, and multiple-choice "On Your Own" exam-style questions.

List Price = $92.95
| CengageBrain Price = $92.49
| College Bookstore Wholesale Price = $68.50

###
CalcLabs with Mathematica for Single Variable Calculus
(ISBN-10: 0840058144 | ISBN-13: 9780840058140)

These comprehensive manuals help students use Maple or Mathematica programs more efficiently. These are available for bundling with your Stewart Calculus text at a special discount.

List Price = $106.95
| CengageBrain Price = $106.49
| College Bookstore Wholesale Price = $79.50

###
Math CourseMate with eBook Instant Access Code
(ISBN-10: 1111674914 | ISBN-13: 9781111674915)

Interested in a simple way to complement your text and course content with study and practice materials? Stewart's Calculus CourseMate from Cengage Learning 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. Stewart's Calculus CourseMate goes beyond the book to deliver what you need! Key features include interactive eBook, quizzes, flashcards, videos, Tools for Enriching Calculus, and Engagement tracker.

List Price = $183.00
| CengageBrain Price = $183.00
| College Bookstore Wholesale Price = $183.00

###
Enhanced WebAssign Multi-Term LOE Instant Access for Calculus
(ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. 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.
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 Cengage Learning Consultant.

List Price = $95.00
| CengageBrain Price = $95.00
| College Bookstore Wholesale Price = $95.00

## 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.**

###
Single Variable Calculus, Hybrid Edition
(ISBN-10: 1111426759 | ISBN-13: 9781111426750)

Reflecting Cengage Learning’s commitment to offering value for students, these new hybrid versions feature the same content and coverage found in the full text while delivering end-of-section exercises online in Enhanced WebAssign®. Access to Enhanced WebAssign and the new media-rich Cengage YouBook is included with every new text, giving you an interactive learning experience with the convenience of a text that is both brief and affordable.
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With SINGLE VARIABLE CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

List Price = $146.95
| College Bookstore Wholesale Price = $108.50

###
Single Variable Calculus, Volume 1
(ISBN-10: 053849784X | ISBN-13: 9780538497848)

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With SINGLE VARIABLE CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

List Price = $172.95
| CengageBrain Price = $137.99
| College Bookstore Wholesale Price = $127.75

###
Single Variable Calculus, Volume 2
(ISBN-10: 0538497858 | ISBN-13: 9780538497855)

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With SINGLE VARIABLE CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

List Price = $172.95
| CengageBrain Price = $137.99
| College Bookstore Wholesale Price = $127.75

###
Student Solutions Manual (Chapters 1-11)
(ISBN-10: 0840049498 | ISBN-13: 9780840049490)

This manual includes worked-out solutions to every odd-numbered exercise in Single Variable Calculus, 7e (Chapters 1-11 of Calculus, 7e).

List Price = $107.95
| CengageBrain Price = $107.49
| College Bookstore Wholesale Price = $79.75

###
Study Guide, SV
(ISBN-10: 0840054092 | ISBN-13: 9780840054098)

Study smarter with the Study Guide for Stewart's Single Variable Calculus, 7E. For each section of the text, the Study Guide provides a brief introduction, a short list of concepts to master, and summary and focus questions with explained answers. "Technology Plus" questions and multiple-choice "On Your Own" exam-style questions help you prepare for exams.

List Price = $92.95
| CengageBrain Price = $92.49
| College Bookstore Wholesale Price = $68.50

###
CalcLabs with Mathematica for Single Variable Calculus
(ISBN-10: 0840058144 | ISBN-13: 9780840058140)

Over the past two decades the wide availability of powerful computational software such as Mathematica ® has had a significant effect upon the way calculus is taught and learned. Remarkably, computations that would have been extraordinary just a few years ago—and certainly unimaginable in the times of Newton, Gauss, and Riemann—can be done easily with a computer and Mathematica. The primary goal of this manual is to show you how Mathematica can help you learn and use calculus. The approach is to use Mathematica as a tool for exploring calculus concepts and the way calculus can be used to solve problems.

List Price = $106.95
| CengageBrain Price = $106.49
| College Bookstore Wholesale Price = $79.50

###
Math CourseMate with eBook Instant Access Code
(ISBN-10: 1111674914 | ISBN-13: 9781111674915)

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. Stewart's Calculus CourseMate includes an interactive eBook with highlighting, note-taking, and glossary, quizzes, flashcards, videos, Tools for Enriching Calculus, and more!

List Price = $183.00
| CengageBrain Price = $183.00
| College Bookstore Wholesale Price = $183.00

###
Enhanced WebAssign Multi-Term LOE Instant Access for Calculus
(ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. 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 = $95.00
| CengageBrain Price = $95.00
| College Bookstore Wholesale Price = $95.00