Chapter 1 Limits and Their Properties. Copyright © Houghton Mifflin Company. All rights reserved.21-2 Figure 1.1.

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Presentation transcript:

Chapter 1 Limits and Their Properties

Copyright © Houghton Mifflin Company. All rights reserved.21-2 Figure 1.1

Copyright © Houghton Mifflin Company. All rights reserved.31-3 Figure 1.3

Copyright © Houghton Mifflin Company. All rights reserved.41-4 Figure 1.4

Copyright © Houghton Mifflin Company. All rights reserved.51-5 Common Types of Behavior Associated with Nonexistence of a Limit

Copyright © Houghton Mifflin Company. All rights reserved.61-6 Definition of Limit

Copyright © Houghton Mifflin Company. All rights reserved.71-7 Theorem 1.1 Some Basic Limits

Copyright © Houghton Mifflin Company. All rights reserved.81-8 Theorem 1.2 Properties of Limits

Copyright © Houghton Mifflin Company. All rights reserved.91-9 Theorem 1.3 Limits of Polynomial and Rational Functions

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.4 The Limit of a Function Involving a Radical

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.5 The Limit of a Composite Function

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.6 Limits of Trigonometric Functions

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.7 Functions That Agree at All But One Point

Copyright © Houghton Mifflin Company. All rights reserved A Strategy for Finding Limits Box

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.8 The Squeeze Theorem and Figure 1.21

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.9 Two Special Trigonometric Limits

Copyright © Houghton Mifflin Company. All rights reserved Figure 1.25

Copyright © Houghton Mifflin Company. All rights reserved Definition of Continuity

Copyright © Houghton Mifflin Company. All rights reserved Figure 1.26

Copyright © Houghton Mifflin Company. All rights reserved Figure 1.28

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.10 The Existence of a Limit

Copyright © Houghton Mifflin Company. All rights reserved Definition of Continuity on a Closed Interval and Figure 1.31

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.11 Properties of Continuity

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.12 Continuity of a Composite Function

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.13 Intermediate Value Theorem

Copyright © Houghton Mifflin Company. All rights reserved Figure 1.35 and Figure 1.36

Copyright © Houghton Mifflin Company. All rights reserved Definition of Infinite Limits and Figure 1.40

Copyright © Houghton Mifflin Company. All rights reserved Definition of Vertical Asymptote

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.14 Vertical Asymptotes

Copyright © Houghton Mifflin Company. All rights reserved Theorem 1.15 Properties of Infinite Limits

Copyright © Houghton Mifflin Company. All rights reserved Definition of Limits at Infinity and Figure 3.34

Copyright © Houghton Mifflin Company. All rights reserved Definition of a Horizontal Asymptote

Copyright © Houghton Mifflin Company. All rights reserved Theorem 3.10 Limits at Infinity

Copyright © Houghton Mifflin Company. All rights reserved Guidelines for Finding Limits at +/- infinity of Rational Functions

Copyright © Houghton Mifflin Company. All rights reserved Definition of Infinite Limits at Infinity