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Chapter 1
Limits and Their Properties
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Figure 1.1
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Figure 1.3
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Figure 1.4
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Common Types of Behavior Associated with Nonexistence of a Limit
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Definition of Limit
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Theorem 1.1 Some Basic Limits
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Theorem 1.2 Properties of Limits
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Theorem 1.3 Limits of Polynomial and Rational Functions
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Theorem 1.4 The Limit of a Function Involving a Radical
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Theorem 1.5 The Limit of a Composite Function
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Theorem 1.6 Limits of Trigonometric Functions
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Theorem 1.7 Functions That Agree at All But One Point
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A Strategy for Finding Limits Box
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Theorem 1.8 The Squeeze Theorem and Figure 1.21
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Theorem 1.9 Two Special Trigonometric Limits
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Figure 1.25
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Definition of Continuity
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Figure 1.26
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Figure 1.28
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Theorem 1.10 The Existence of a Limit
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Definition of Continuity on a Closed Interval and Figure 1.31
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Theorem 1.11 Properties of Continuity
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Theorem 1.12 Continuity of a Composite Function
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Theorem 1.13 Intermediate Value Theorem
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Figure 1.35 and Figure 1.36
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Definition of Infinite Limits and Figure 1.40
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Definition of Vertical Asymptote
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Theorem 1.14 Vertical Asymptotes
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Theorem 1.15 Properties of Infinite Limits
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Definition of Limits at Infinity and Figure 3.34
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Definition of a Horizontal Asymptote
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Theorem 3.10 Limits at Infinity
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Guidelines for Finding Limits at +/- infinity of Rational Functions
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Definition of Infinite Limits at Infinity