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Functions and Graphs

Maxima and Minima

Review of Functions

The Mean Value Theorem

Basic Classes of Functions

The First Derivative Test

Trigonometric Functions

The Second Derivative Test and Curve Sketching

Inverse Functions

L’Hôpital’s Rule

Exponential and Logarithmic Functions

Applied Optimization Problems

Chapter 1 Review Exercises

Newton’s Method

Limits

Chapter 4 Review Exercises

The Limit of a Function and Limit Laws

Integration

The Precise Definition of a Limit

Antiderivatives

One-Sided Limits

Approximating Areas with Limits of Finite Sums

Continuity

The Definite Integral

Limits at Infinity; Asymptotes of Graphs

The Fundamental Theorem of Calculus

Chapter 2 Review Exercises

Substitution with Indefinite Integrals

Derivatives

Substitution with Definite Integrals

Defining the Derivative

Chapter 5 Review Exercises

The Derivative as a Function

Applications of Integration

Differentiation Rules

Areas between Curves

Derivatives as Rates of Change

Determining Volumes by Slicing

Derivatives of Trigonometric Functions

Volumes of Revolution: Cylindrical Shells

The Chain Rule

Arc Length of a Curve and Surface Area

Implicit Differentiation

Physical Applications

Derivatives of Inverse and Logarithmic Functions

Moments and Centers of Mass

Derivatives of Inverse Trigonometric Functions

Integrals, Exponential Functions, and Logarithms

Related Rates

Exponential Growth and Decay

Linear Approximations and Differentials

Calculus of the Hyperbolic Functions

Chapter 3 Review Exercises

Chapter 6 Review Excercises

Applications of Derivatives