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Main Body

Linear Approximations and Differentials

Page 1

Maxima and Minima

Functions and Graphs

The Mean Value Theorem

Review of Functions

Derivatives and the Shape of a Graph

Basic Classes of Functions

Limits at Infinity and Asymptotes

Trigonometric Functions

Applied Optimization Problems

Inverse Functions

L’Hôpital’s Rule

Exponential and Logarithmic Functions

Newton’s Method

Chapter 1

Antiderivatives

Limits

Integration

A Preview of Calculus

Introduction

The Limit of a Function

Approximating Areas

The Limit Laws

The Definite Integral

Continuity

The Fundamental Theorem of Calculus

The Precise Definition of a Limit

Integration Formulas and the Net Change Theorem

Derivatives

Substitution

Introduction

Integrals Involving Exponential and Logarithmic Functions

Defining the Derivative

Integrals Resulting in Inverse Trigonometric Functions

The Derivative as a Function

Applications of Integration

Differentiation Rules

Introduction

Derivatives as Rates of Change

Areas between Curves

Derivatives of Trigonometric Functions

Determining Volumes by Slicing

The Chain Rule

Volumes of Revolution: Cylindrical Shells

Derivatives of Inverse Functions

Arc Length of a Curve and Surface Area

Implicit Differentiation

Physical Applications

Derivatives of Exponential and Logarithmic Functions

Moments and Centers of Mass

Applications of Derivatives

Integrals, Exponential Functions, and Logarithms

Introduction

Exponential Growth and Decay

Related Rates

Calculus of the Hyperbolic Functions