Professional

# Calculus: An Applied Approach, 9th Edition

### Overview

Designed specifically for business, economics, or life/social sciences majors, CALCULUS: AN APPLIED APPROACH, Ninth Edition, motivates students while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show students the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to students' diverse interests. The Ninth Edition builds upon its applications emphasis through updated exercises and relevant examples. Pedagogical features--from algebra review to study tips--provide extra guidance and practice.

### Features and Benefits

• Every section begins with a list of objectives that highlights the learning outcomes of that section and provides instructors with a tool for lesson planning.
• Appearing in the middle of each chapter, Mid-Chapter Quizzes are single-page tests that let students practice skills and concepts learned in the chapter. This opportunity for self-assessment helps uncover potential weaknesses that might require further review of the material.
• Revised! Section-ending Business Capsules and accompanying exercises address business situations related to the mathematical concepts covered in the chapter.
• Revised! At the beginning of each exercise set, Skills Warm Up exercises give students practice of skills covered in previous sections that are used in the exercise set; answers are provided at the back of the text to reinforce understanding.
• Updated! The Exercise Sets have been revised based on actual student usage data to improve student comprehension. Approximately 5,000 exercises progress from skill-development problems to more challenging, real-world applications--all of which can be customized to the difficulty level of the instructor's choice.
• A wide variety of relevant examples--each of which is titled for easy reference--includes solutions presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Examples that illustrate real-life situations are identified with an icon.
• For instructors who wish to incorporate technology, optional Tech Tutor boxes provide guidance on using technology to ease lengthy calculations, present a graphical solution, or discuss where using technology can lead to misleading or wrong solutions. In addition, exercises requiring technology are identified with a graphing calculator icon.

1. FUNCTIONS, GRAPHS, AND LIMITS.
The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity.
2. DIFFERENTIATION.
The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule.
Higher-Order Derivatives. Implicit Differentiation. Related Rates.
3. APPLICATIONS OF THE DERIVATIVE.
Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test. Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay.
5. INTEGRATION AND ITS APPLICATIONS.
Antiderivatives and Indefinite Integrals. Integration by Substitution and the General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum.
6. TECHNIQUES OF INTEGRATION.
Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals.
7. FUNCTIONS OF SEVERAL VARIABLES.
The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane.
Applications of Double Integrals.
8. TRIGONOMETRIC FUNCTIONS.
Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. Integrals of Trigonometric Functions.
9. PROBABILITY AND CALCULUS.
Discrete Probability. Continuous Random Variables. Expected Value and Variance.
10. SERIES AND TAYLOR POLYNOMIALS.
Sequences. Series and Convergence. p-Series and the Ratio Test. Power Series and Taylor's Theorem. Taylor Polynomials. Newton's Method.
11. DIFFERENTIAL EQUATIONS.
Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations.
Appendix A. Precalculus Review.
The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization.
Appendix B. Alternative Introduction to the Fundamental Theorem of Calculus.
Appendix C. Formulas.

### What's New

• New! A new closing chapter, "Differential Equations," includes topics on solutions of differential equations, separation of variables, and first-order linear differential equations.
• New! A Summarize feature guides students in creating section-level concept summaries-- helping them process and organize key concepts while providing a valuable study tool.
• New! How Do You See It? exercises ask students to draw conclusions about information presented visually. Requiring little or no calculation, these exercises check students' conceptual understanding of key concepts.
• New and Updated! Projects, which appear in selected sections, connect real-life data and applications and give your students the opportunity to generate and analyze mathematical models from large data sets.
• New! 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.

• ### Hybrid Edition

ISBN-10: 1133115004 | ISBN-13: 9781133115007

List Price = \$140.95  | CengageBrain Price = \$140.95

### Bundle: Text + Enhanced WebAssign with eBook LOE Printed Access Card for One-Term Math and Science + Custom Enrichment Module: Enhanced WebAssign - Start Smart Guide for Students

ISBN-10: 1133798217  | ISBN-13: 9781133798217

List Price = \$364.95

### Bundle: Text + Student Solutions Manual

ISBN-10:  1133798535  | ISBN-13:  9781133798538

List Price = \$435.95  | CengageBrain Price = \$435.95

### Printed Text + Enhanced WebAssign - Start Smart Guide for Students + Enhanced WebAssign Instant Access for Calculus, Multi-Term Course

ISBN-10:  1305593340  | ISBN-13:  9781305593343

List Price = \$364.95  | CengageBrain Price = \$364.95

### Printed Text + CourseMate Instant Access

ISBN-10:  1305615859  | ISBN-13:  9781305615854

List Price = \$215.95  | CengageBrain Price = \$215.95

### Printed Text + Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses

ISBN-10:  1337068497 | ISBN-13:  9781337068499

List Price = \$344.95

## Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

### Instructor Supplements

#### Calculus: An Applied Approach, Hybrid  (ISBN-10: 1133115004 | ISBN-13: 9781133115007)

Reflecting Cengage Learning’s commitment to offering value for students, these new hybrid versions feature the instructional presentation found in CALCULUS AN APPLIED APPROACH, Ninth Edition while delivering all of end-of-section exercises online in Enhanced WebAssign®. Access to Enhanced WebAssign® includes the premium eBook, giving you an interactive learning experience with the convenience of a text that is both brief and affordable. Designed specifically for business, economics, or life/social sciences majors, CALCULUS: AN APPLIED APPROACH, Ninth Edition, motivates your study while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show you the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to diverse interests. The Ninth Edition builds upon its applications emphasis through updated exercises and relevant examples. Pedagogical features—from algebra review to study tips—continue to provide you with extra guidance and practice.

List Price = \$140.95  | CengageBrain Price = \$140.95  | College Bookstore Wholesale Price = \$104.50

#### Brief Calculus: An Applied Approach  (ISBN-10: 1133109489 | ISBN-13: 9781133109488)

Designed specifically for business, economics, or life/social sciences majors, BRIEF CALCULUS: AN APPLIED APPROACH, Ninth Edition, motivates students while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show students the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to students' diverse interests. The Ninth Edition builds upon its applications emphasis through updated exercises and relevant examples. Pedagogical features--from algebra review to study tips--provide extra guidance and practice.

List Price = \$306.95  | CengageBrain Price = \$306.95  | College Bookstore Wholesale Price = \$230.25

#### CourseMate Instant Access  (ISBN-10: 1133508758 | ISBN-13: 9781133508755)

Cengage Learning's CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Maximize your course success with the integrated eBook and chapter-specific learning tools that include flashcards, quizzes, videos, and more in your CourseMate. Key Features: Interactive eBook, Engagement Tracker, Learning Objectives, Tutorial Quizzes, Glossary and Flashcards, and Web Links and References.

List Price = \$270.00  | CengageBrain Price = \$270.00  | College Bookstore Wholesale Price = \$270.00

#### Complete Solutions Manual  (ISBN-10: 1133364322 | ISBN-13: 9781133364320)

Contains fully worked-out solutions to all exercises in the text.

#### Student Solutions Manual  (ISBN-10: 113311279X | ISBN-13: 9781133112792)

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.

List Price = \$97.95  | CengageBrain Price = \$97.95  | College Bookstore Wholesale Price = \$73.50

#### Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses  (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 = \$94.00  | CengageBrain Price = \$94.00  | College Bookstore Wholesale Price = \$94.00

#### 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 = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50

### Student Supplements

#### Calculus: An Applied Approach, Hybrid  (ISBN-10: 1133115004 | ISBN-13: 9781133115007)

Reflecting Cengage Learning’s commitment to offering value for students, these new hybrid versions feature the instructional presentation found in CALCULUS AN APPLIED APPROACH, Ninth Edition while delivering all of end-of-section exercises online in Enhanced WebAssign®. Access to Enhanced WebAssign® includes the premium eBook, giving you an interactive learning experience with the convenience of a text that is both brief and affordable. Designed specifically for business, economics, or life/social sciences majors, CALCULUS: AN APPLIED APPROACH, Ninth Edition, motivates your study while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show you the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to diverse interests. The Ninth Edition builds upon its applications emphasis through updated exercises and relevant examples. Pedagogical features—from algebra review to study tips—continue to provide you with extra guidance and practice.

List Price = \$140.95  | CengageBrain Price = \$140.95  | College Bookstore Wholesale Price = \$104.50

#### Brief Calculus: An Applied Approach  (ISBN-10: 1133109489 | ISBN-13: 9781133109488)

Designed specifically for business, economics, or life/social sciences majors, BRIEF CALCULUS: AN APPLIED APPROACH, Ninth Edition, motivates students while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show students the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to students' diverse interests. The Ninth Edition builds upon its applications emphasis through updated exercises and relevant examples. Pedagogical features--from algebra review to study tips--provide extra guidance and practice.

List Price = \$306.95  | CengageBrain Price = \$306.95  | College Bookstore Wholesale Price = \$230.25

#### CourseMate Instant Access  (ISBN-10: 1133508758 | ISBN-13: 9781133508755)

Cengage Learning's CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Maximize your course success with the integrated eBook and chapter-specific learning tools that include flashcards, quizzes, videos, and more in your CourseMate. Key Features: Interactive eBook, Engagement Tracker, Learning Objectives, Tutorial Quizzes, Glossary and Flashcards, and Web Links and References.

List Price = \$270.00  | CengageBrain Price = \$270.00  | College Bookstore Wholesale Price = \$270.00

#### Student Solutions Manual  (ISBN-10: 113311279X | ISBN-13: 9781133112792)

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.

List Price = \$97.95  | CengageBrain Price = \$97.95  | College Bookstore Wholesale Price = \$73.50

#### Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses  (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 = \$94.00  | CengageBrain Price = \$94.00  | College Bookstore Wholesale Price = \$94.00

Flashcards designed to work with your text can help you to review and learn essential terms and key concepts. Interactive flashcards include terms and definitions for each chapter. This is instant access product; at the completion of your purchase, simply go to "My Home" and gain immediate access to your product. Note: If you have purchased CourseMate for your title, flash cards are already included.

List Price = \$4.25  | College Bookstore Wholesale Price = \$4.25

#### 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 = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50

Interactive practice quizzes designed to work with your text can help you to review and learn essential terms and key concepts. True/false and multiple choice questions are included for each chapter. Check your score and take quizzes again if needed. A reference for where to find more material in the text is included with each answer. This is instant access product; at the completion of your purchase, simply go to "My Home" and gain immediate access to your product. Note: If you have purchased CourseMate for your title, flash cards are already included.

List Price = \$5.25  | College Bookstore Wholesale Price = \$5.25

Interactive practice quizzes and flashcards designed to work with your text can help you to review and learn essential terms and key concepts. Flashcards contain terms and definitions for each chapter. Practice quizzes consist of true/false and multiple choice questions for each chapter. Check your score and take quizzes again if needed. A reference for where to find more material in the text is included with each answer. This is instant access product; at the completion of your purchase, simply go to "My Home" and gain immediate access to your product. Note: If you have purchased CourseMate for your title, practice quizzes and flashcards are already included.

List Price = \$6.25  | College Bookstore Wholesale Price = \$6.25

## Meet the Author

### Ron Larson

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.