## Description

This accessible text is designed to help readers help themselves to excel. The content is organized into two parts: (1) A Library of Elementary Functions (Chapters 1–2) and (2) Calculus (Chapters 3–9). The book’s overall approach, refined by the authors’ experience with large sections of college freshmen, addresses the challenges of teaching and learning when readers’ prerequisite knowledge varies greatly. Reader-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for today’s students and instructors.

## Table of Contents

**Part One: A Library of Elementary Functions**

**Chapter 1: Linear Equations and Graphs**

1-1 Linear Equations and Inequalities

1-2 Graphs and Lines

1-3 Linear Regression

Chapter 1 Review

Review Exercise

**Chapter 2: Functions and Graphs**

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Polynomial and Rational Functions

2-5 Exponential Functions

2-6 Logarithmic Functions

Chapter 2 Review

Review Exercise

**Part Two: Calculus**

**Chapter 3: Limits and the Derivative**

3-1 Introduction to Limits

3-2 Infinite Limits and Limits at Infinity

3-3 Continuity

3-4 The Derivative

3-5 Basic Differentiation Properties

3-6 Differentials

3-7 Marginal Analysis in Business and Economics

Chapter 3 Review

Review Exercise

**Chapter 4: Additional Derivative Topics**

4-1 The Constant e and Continuous Compound Interest

4-2 Derivatives of Exponential and Logarithmic Functions

4-3 Derivatives of Products and Quotients

4-4 The Chain Rule

4-5 Implicit Differentiation

4-6 Related Rates

4-7 Elasticity of Demand

Chapter 4 Review

Review Exercise

**Chapter 5: Graphing and Optimization**

5-1 First Derivative and Graphs

5-2 Second Derivative and Graphs

5-3 L'Hopital's Rule

5-4 Curve Sketching Techniques

5-5 Absolute Maxima and Minima

5-6 Optimization

Chapter 5 Review

Review Exercise

**Chapter 6: Integration**

6-1 Antiderivatives and Indefinite Integrals

6-2 Integration by Substitution

6-3 Differential Equations; Growth and Decay

6-4 The Definite Integral

6-5 The Fundamental Theorem of Calculus

Chapter 6 Review

Review Exercise

**Chapter 7: Additional Integration Topics**

7-1 Area Between Curves

7-2 Applications in Business and Economics

7-3 Integration by Parts

7-4 Integration Using Tables

Chapter 7 Review

Review Exercise

**Chapter 8: Multivariable Calculus**

8-1 Functions of Several Variables

8-2 Partial Derivatives

8-3 Maxima and Minima

8-4 Maxima and Minima Using Lagrange Multipliers

8-5 Method of Least Squares

8-6 Double Integrals Over Rectangular Regions

8-7 Double Integrals Over More General Regions

Chapter 8 Review

Review Exercise

**Chapter 9: Trigonometric Functions**

9-1 Trigonometric Functions Review

9-2 Derivatives of Trigonometric Functions

9-3 Integration of Trigonometric Functions

Chapter 9 Review

Review Exercise

**Appendixes**

** **

**Appendix A: Basic Algebra Review **

Self-Test on Basic Algebra

A-1 Algebra and Real Numbers

A-2 Operations on Polynomials

A-3 Factoring Polynomials

A-4 Operations on Rational Expressions

A-5 Integer Exponents and Scientific Notation

A-6 Rational Exponents and Radicals

A-7 Quadratic Equations

**Appendix B: Special Topics**

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 Binomial Theorem

** **

**Appendix C: Tables**

Table I Basic Geometric Formulas

Table II Integration Formulas

**Answers**

**Index**

**Applications Index**

**A Library of Elementary Functions**

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