Table of Contents

Chapter 1 • Functions and Graphs
 Polynomial Functions
 Domain and Range of a Rational Function
 Radical Functions
 Domain and Range from Function Graphs
 Composite Functions
 Combining Functions
 Equation of a Straight Line: Standard and Point–Slope Forms
 Linear Functions in Different Forms
 Slopes and Intercepts of Linear Functions
 Degree and Coefficient of Polynomials
 Conversion between Radians and Degrees
 Evaluating Trigonometric Functions Using Periodic Functions
 Trigonometric Ratios in Right Triangles
 Simplifying Trigonometric Expressions Using Trigonometric Identities
 Simple Trigonometric Equations
 Inverse of a Function
 Graphs of Inverses of Functions
 Graphs of Exponential Functions
 Exponential Functions
 Graphs of Logarithmic Functions
 Solving Exponential Equations Using Logarithms
 Natural Exponential Equations
 Converting between Logarithmic and Exponential Forms
 Logarithmic Equations with Like Bases
 Chapter 2 • Limits

Chapter 3 • Derivatives
 Definition of the Derivative
 The Differentiability of a Function
 Combining the Product, Quotient, and Chain Rules
 Power Rule of Derivatives
 The Product Rule
 The Quotient Rule
 Differentiation of Trigonometric Functions
 The Chain Rule
 Derivatives of Inverse Trigonometric Functions
 Implicit Differentiation
 Differentiation of Exponential Functions
 Differentiation of Logarithmic Functions

Chapter 4 • Applications of Derivatives
 Related Rates
 Linear Approximation
 Critical Points and Local Extrema of a Function
 Absolute Extrema
 The Mean Value Theorem
 Second Derivative Test for Local Extrema
 Concavity and Points of Inflection
 Graphing Using Derivatives
 Limits at Infinity and Unbounded Limits
 Horizontal and Vertical Asymptotes of a Function
 Oblique Asymptotes
 Optimization Using Derivatives
 L’Hôpital’s Rule
 Indeterminate Forms and L’Hôpital’s Rule
 Antiderivatives
 Indefinite Integrals: The Power Rule
 Indefinite Integrals and Initial Value Problems

Chapter 5 • Integration
 Riemann Sums
 Riemann Sums and Sigma Notation
 Definite Integrals as Limits of Riemann Sums
 The Fundamental Theorem of Calculus: Evaluating Definite Integrals
 Average Value of a Function
 The Fundamental Theorem of Calculus: Functions Defined by Integrals
 The Net Change Theorem
 Properties of Definite Integrals
 Integration by Substitution: Indefinite Integrals
 Integrals Resulting in Logarithmic Functions
 Integrals Resulting in Inverse Trigonometric Functions

Chapter 6 • Applications of Integration
 Area between a Curve and a Line
 Area between Curves
 Volumes of Solids of Revolution Using the Shell Method
 Volumes of Solids of Revolution Using the Disk and Washer Methods
 Arc Length by Integration
 Surface Area of a Solid of Revolution
 Indefinite Integrals: Exponential and Reciprocal Functions
 Exponential Growth and Decay Models
 Exponential Growth and Decay
 Derivatives of Hyperbolic Functions
 Derivatives of Inverse Hyperbolic Functions
 Hyperbolic Functions