Limits and Their Properties

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Limits and Their Properties
Chapter 1 Limits and Their Properties

Common Types of Behavior Associated with Nonexistence of a Limit

Theorem 1.1 Some Basic Limits

Theorem 1.2 Properties of Limits

Theorem 1.3 Limits of Polynomial and Rational Functions

Theorem 1.4 The Limit of a Function Involving a Radical

Theorem 1.5 The Limit of a Composite Function

Theorem 1.6 Limits of Trigonometric Functions

Theorem 1.7 Functions That Agree at All But One Point

A Strategy for Finding Limits Box

Theorem 1.8 The Squeeze Theorem and Figure 1.21

Theorem 1.9 Two Special Trigonometric Limits

Definition of Continuity

Theorem 1.10 The Existence of a Limit

Definition of Continuity on a Closed Interval and Figure 1.31

Theorem 1.11 Properties of Continuity

Theorem 1.12 Continuity of a Composite Function

Theorem 1.13 Intermediate Value Theorem

Definition of Infinite Limits and Figure 1.40

Definition of Vertical Asymptote

Theorem 1.14 Vertical Asymptotes

Theorem 1.15 Properties of Infinite Limits

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