Chapter 1 Limits and Their Properties. Copyright Houghton Mifflin Company. All rights reserved.21-2...

Chapter 1

Limits and Their Properties

Copyright © Houghton Mifflin Company. All rights reserved. 21-2

Figure 1.1


Figure 1.3


Figure 1.4


Common Types of Behavior Associated with Nonexistence of a Limit


Definition of 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


Figure 1.25


Definition of Continuity


Figure 1.26


Figure 1.28


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


Figure 1.35 and Figure 1.36


Definition of Infinite Limits and Figure 1.40


Definition of Vertical Asymptote


Theorem 1.14 Vertical Asymptotes


Theorem 1.15 Properties of Infinite Limits


Definition of Limits at Infinity and Figure 3.34


Definition of a Horizontal Asymptote


Theorem 3.10 Limits at Infinity


Guidelines for Finding Limits at +/- infinity of Rational Functions


Definition of Infinite Limits at Infinity

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