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by Ron Larson and Bruce H. Edwards

Edition: 7TH 06Copyright: 2006

Publisher: Houghton Mifflin Harcourt

Published: 2006

International: No

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Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 7/e, addresses students' weak math skills through added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.

The Seventh Edition places a new emphasis on algebra review through Algebra Tips at point of use throughout the chapter and Algebra Review at the end of each chapter. This edition also builds on a proven emphasis on applications; updates and increases the coverage of technology at point of use; and includes sample post-graduation exam questions.

Approximately 6,000 exercises--progress from skill-development problems to more challenging, real-world application questions--are easily customized to the difficulty level of the instructor's choice. In addition, a number of relevant exercises from textbooks in other disciplines--such as biology, chemistry, economics, finance, geology, physics, and psychology--to show students that they will use calculus in future courses outside of the math curriculum.

- Algebra Review offers students algebraic support at point of use and at the end of the chapter. The end-of-chapter Algebra Review illustrate the key algebraic concepts called out in the Algebra Reviews used throughout the chapter. This feature is designed to help students who may have weak algebra skills and need help as they take a calculus course.
- Prerequisite Review exercises at the beginning of each exercise set help students review skills covered in previous sections. The answers are provided at the back of the text, enabling students to check their work. Review Exercises are also included at the end of each chapter and offer students the opportunity for additional practice and review.
- Discovery Projects expose students to concepts before the topic is covered in the text. This allows students to explore the concept on their own, making them more likely to remember the results.
- Take Another Look, appearing just before each section exercise set, asks students to look back at one or more concepts presented in the section. The questions in these sections are designed to enhance understanding of key ideas.
- Post-Graduation Exam Questions appear at the end of each chapter. They include sample questions representative of the types of questions on various standardized tests (i.e. GMAT, CPA exams, GRE, College Level Academic Skills Test). These questions challenge students and provide additional practice.
- Business Capsules appear at the end of numerous sections. Along with accompanying exercises, these features deal with business situations related to the mathematical concepts covered in the chapter. This feature allows students to see the relevance of what they are learning, and the importance of everyday mathematics.
- Ready to use and easy to integrate into your calculus course, Eduspace, powered by Blackboard, brings your students quality homework, tutorials, and testing while saving you time. Browser-based, algorithmically generated homework problems are scored for you automatically. You determine whether the grade is recorded and how much each assignment counts toward a final grade.

**A Precalculus Review**

0.1 The Real Line and Order

0.2 Absolute Value and Distance on the Real Line

0.3 Exponents and Radicals

0.4 Factoring Polynomials

0.5 Fractions and Rationalization

**1. Functions, Graphs, and Limits**

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**2. Differentiation**

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**3. Applications of the Derivative**

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum

5.7 Volumes of Solids of Revolution

**6. Techniques of Integration**

6.1 Integration by Substitution

6.2 Integration by Parts and Present Value

6.3 Partial Fractions and Logistic Growth

6.4 Integration Tables and Completing the Square

6.5 Numerical Integration

6.6 Improper Integrals

**7. Functions of Several Variables**

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**8. Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Trigonometric Functions

8.3 Graphs of Trigonometric Functions

8.4 Derivatives of Trigonometric Functions

8.5 Integrals of Trigonometric Functions

8.6 L'Hôpital's Rule

**9. Probability and Calculus**

9.1 Discrete Probability

9.2 Continuous Random Variables

9.3 Expected Value and Variance

**10. Series and Taylor Polynomials**

10.1 Sequences

10.2 Series and Convergence

10.3 p-Series and the Ratio Test

10.4 Power Series and Taylor's Theorem

10.5 Taylor Polynomials

10.6 Newton's Method

**Appendices**

A. Alternate Introduction to the Fundamental Theorem of Calculus

B. Formulas

C. Differential Equations

C.1 Solutions of Differential Equations

C.2 Separation of Variables

C.3 First-Order Linear Differential Equations

C.4 Applications of Differential Equations

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Summary

Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 7/e, addresses students' weak math skills through added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.

The Seventh Edition places a new emphasis on algebra review through Algebra Tips at point of use throughout the chapter and Algebra Review at the end of each chapter. This edition also builds on a proven emphasis on applications; updates and increases the coverage of technology at point of use; and includes sample post-graduation exam questions.

Approximately 6,000 exercises--progress from skill-development problems to more challenging, real-world application questions--are easily customized to the difficulty level of the instructor's choice. In addition, a number of relevant exercises from textbooks in other disciplines--such as biology, chemistry, economics, finance, geology, physics, and psychology--to show students that they will use calculus in future courses outside of the math curriculum.

- Algebra Review offers students algebraic support at point of use and at the end of the chapter. The end-of-chapter Algebra Review illustrate the key algebraic concepts called out in the Algebra Reviews used throughout the chapter. This feature is designed to help students who may have weak algebra skills and need help as they take a calculus course.
- Prerequisite Review exercises at the beginning of each exercise set help students review skills covered in previous sections. The answers are provided at the back of the text, enabling students to check their work. Review Exercises are also included at the end of each chapter and offer students the opportunity for additional practice and review.
- Discovery Projects expose students to concepts before the topic is covered in the text. This allows students to explore the concept on their own, making them more likely to remember the results.
- Take Another Look, appearing just before each section exercise set, asks students to look back at one or more concepts presented in the section. The questions in these sections are designed to enhance understanding of key ideas.
- Post-Graduation Exam Questions appear at the end of each chapter. They include sample questions representative of the types of questions on various standardized tests (i.e. GMAT, CPA exams, GRE, College Level Academic Skills Test). These questions challenge students and provide additional practice.
- Business Capsules appear at the end of numerous sections. Along with accompanying exercises, these features deal with business situations related to the mathematical concepts covered in the chapter. This feature allows students to see the relevance of what they are learning, and the importance of everyday mathematics.
- Ready to use and easy to integrate into your calculus course, Eduspace, powered by Blackboard, brings your students quality homework, tutorials, and testing while saving you time. Browser-based, algorithmically generated homework problems are scored for you automatically. You determine whether the grade is recorded and how much each assignment counts toward a final grade.

Table of Contents

**A Precalculus Review**

0.1 The Real Line and Order

0.2 Absolute Value and Distance on the Real Line

0.3 Exponents and Radicals

0.4 Factoring Polynomials

0.5 Fractions and Rationalization

**1. Functions, Graphs, and Limits**

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**2. Differentiation**

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**3. Applications of the Derivative**

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum

5.7 Volumes of Solids of Revolution

**6. Techniques of Integration**

6.1 Integration by Substitution

6.2 Integration by Parts and Present Value

6.3 Partial Fractions and Logistic Growth

6.4 Integration Tables and Completing the Square

6.5 Numerical Integration

6.6 Improper Integrals

**7. Functions of Several Variables**

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**8. Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Trigonometric Functions

8.3 Graphs of Trigonometric Functions

8.4 Derivatives of Trigonometric Functions

8.5 Integrals of Trigonometric Functions

8.6 L'Hôpital's Rule

**9. Probability and Calculus**

9.1 Discrete Probability

9.2 Continuous Random Variables

9.3 Expected Value and Variance

**10. Series and Taylor Polynomials**

10.1 Sequences

10.2 Series and Convergence

10.3 p-Series and the Ratio Test

10.4 Power Series and Taylor's Theorem

10.5 Taylor Polynomials

10.6 Newton's Method

**Appendices**

A. Alternate Introduction to the Fundamental Theorem of Calculus

B. Formulas

C. Differential Equations

C.1 Solutions of Differential Equations

C.2 Separation of Variables

C.3 First-Order Linear Differential Equations

C.4 Applications of Differential Equations

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2006

International: No

Published: 2006

International: No

Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 7/e, addresses students' weak math skills through added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.

The Seventh Edition places a new emphasis on algebra review through Algebra Tips at point of use throughout the chapter and Algebra Review at the end of each chapter. This edition also builds on a proven emphasis on applications; updates and increases the coverage of technology at point of use; and includes sample post-graduation exam questions.

Approximately 6,000 exercises--progress from skill-development problems to more challenging, real-world application questions--are easily customized to the difficulty level of the instructor's choice. In addition, a number of relevant exercises from textbooks in other disciplines--such as biology, chemistry, economics, finance, geology, physics, and psychology--to show students that they will use calculus in future courses outside of the math curriculum.

- Algebra Review offers students algebraic support at point of use and at the end of the chapter. The end-of-chapter Algebra Review illustrate the key algebraic concepts called out in the Algebra Reviews used throughout the chapter. This feature is designed to help students who may have weak algebra skills and need help as they take a calculus course.
- Prerequisite Review exercises at the beginning of each exercise set help students review skills covered in previous sections. The answers are provided at the back of the text, enabling students to check their work. Review Exercises are also included at the end of each chapter and offer students the opportunity for additional practice and review.
- Discovery Projects expose students to concepts before the topic is covered in the text. This allows students to explore the concept on their own, making them more likely to remember the results.
- Take Another Look, appearing just before each section exercise set, asks students to look back at one or more concepts presented in the section. The questions in these sections are designed to enhance understanding of key ideas.
- Post-Graduation Exam Questions appear at the end of each chapter. They include sample questions representative of the types of questions on various standardized tests (i.e. GMAT, CPA exams, GRE, College Level Academic Skills Test). These questions challenge students and provide additional practice.
- Business Capsules appear at the end of numerous sections. Along with accompanying exercises, these features deal with business situations related to the mathematical concepts covered in the chapter. This feature allows students to see the relevance of what they are learning, and the importance of everyday mathematics.
- Ready to use and easy to integrate into your calculus course, Eduspace, powered by Blackboard, brings your students quality homework, tutorials, and testing while saving you time. Browser-based, algorithmically generated homework problems are scored for you automatically. You determine whether the grade is recorded and how much each assignment counts toward a final grade.

**A Precalculus Review**

0.1 The Real Line and Order

0.2 Absolute Value and Distance on the Real Line

0.3 Exponents and Radicals

0.4 Factoring Polynomials

0.5 Fractions and Rationalization

**1. Functions, Graphs, and Limits**

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**2. Differentiation**

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**3. Applications of the Derivative**

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum

5.7 Volumes of Solids of Revolution

**6. Techniques of Integration**

6.1 Integration by Substitution

6.2 Integration by Parts and Present Value

6.3 Partial Fractions and Logistic Growth

6.4 Integration Tables and Completing the Square

6.5 Numerical Integration

6.6 Improper Integrals

**7. Functions of Several Variables**

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**8. Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Trigonometric Functions

8.3 Graphs of Trigonometric Functions

8.4 Derivatives of Trigonometric Functions

8.5 Integrals of Trigonometric Functions

8.6 L'Hôpital's Rule

**9. Probability and Calculus**

9.1 Discrete Probability

9.2 Continuous Random Variables

9.3 Expected Value and Variance

**10. Series and Taylor Polynomials**

10.1 Sequences

10.2 Series and Convergence

10.3 p-Series and the Ratio Test

10.4 Power Series and Taylor's Theorem

10.5 Taylor Polynomials

10.6 Newton's Method

**Appendices**

A. Alternate Introduction to the Fundamental Theorem of Calculus

B. Formulas

C. Differential Equations

C.1 Solutions of Differential Equations

C.2 Separation of Variables

C.3 First-Order Linear Differential Equations

C.4 Applications of Differential Equations