Chapter 1 Limits and Their Properties Figure 1

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Chapter 1 Limits and Their Properties

Chapter 1 Limits and Their Properties

Figure 1. 1 Copyright © Houghton Mifflin Company. All rights reserved. 2

Figure 1. 1 Copyright © Houghton Mifflin Company. All rights reserved. 2

Figure 1. 3 Copyright © Houghton Mifflin Company. All rights reserved. 3

Figure 1. 3 Copyright © Houghton Mifflin Company. All rights reserved. 3

Figure 1. 4 Copyright © Houghton Mifflin Company. All rights reserved. 4

Figure 1. 4 Copyright © Houghton Mifflin Company. All rights reserved. 4

Common Types of Behavior Associated with Nonexistence of a Limit Copyright © Houghton Mifflin

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

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

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

Theorem 1. 1 Some Basic Limits Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 1. 1 Some Basic Limits Copyright © Houghton Mifflin Company. All rights reserved. 7

Theorem 1. 2 Properties of Limits Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 1. 2 Properties of Limits Copyright © Houghton Mifflin Company. All rights reserved. 8

Theorem 1. 3 Limits of Polynomial and Rational Functions Copyright © Houghton Mifflin Company.

Theorem 1. 3 Limits of Polynomial and Rational Functions Copyright © Houghton Mifflin Company. All rights reserved. 9

Theorem 1. 4 The Limit of a Function Involving a Radical Copyright © Houghton

Theorem 1. 4 The Limit of a Function Involving a Radical Copyright © Houghton Mifflin Company. All rights reserved. 10

Theorem 1. 5 The Limit of a Composite Function Copyright © Houghton Mifflin Company.

Theorem 1. 5 The Limit of a Composite Function Copyright © Houghton Mifflin Company. All rights reserved. 11

Theorem 1. 6 Limits of Trigonometric Functions Copyright © Houghton Mifflin Company. All rights

Theorem 1. 6 Limits of Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 12

Theorem 1. 7 Functions That Agree at All But One Point Copyright © Houghton

Theorem 1. 7 Functions That Agree at All But One Point Copyright © Houghton Mifflin Company. All rights reserved. 13

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

A Strategy for Finding Limits Box Copyright © Houghton Mifflin Company. All rights reserved. 14

Theorem 1. 8 The Squeeze Theorem and Figure 1. 21 Copyright © Houghton Mifflin

Theorem 1. 8 The Squeeze Theorem and Figure 1. 21 Copyright © Houghton Mifflin Company. All rights reserved. 15

Theorem 1. 9 Two Special Trigonometric Limits Copyright © Houghton Mifflin Company. All rights

Theorem 1. 9 Two Special Trigonometric Limits Copyright © Houghton Mifflin Company. All rights reserved. 16

Figure 1. 25 Copyright © Houghton Mifflin Company. All rights reserved. 17

Figure 1. 25 Copyright © Houghton Mifflin Company. All rights reserved. 17

Definition of Continuity Copyright © Houghton Mifflin Company. All rights reserved. 18

Definition of Continuity Copyright © Houghton Mifflin Company. All rights reserved. 18

Figure 1. 26 Copyright © Houghton Mifflin Company. All rights reserved. 19

Figure 1. 26 Copyright © Houghton Mifflin Company. All rights reserved. 19

Figure 1. 28 Copyright © Houghton Mifflin Company. All rights reserved. 20

Figure 1. 28 Copyright © Houghton Mifflin Company. All rights reserved. 20

Theorem 1. 10 The Existence of a Limit Copyright © Houghton Mifflin Company. All

Theorem 1. 10 The Existence of a Limit Copyright © Houghton Mifflin Company. All rights reserved. 21

Definition of Continuity on a Closed Interval and Figure 1. 31 Copyright © Houghton

Definition of Continuity on a Closed Interval and Figure 1. 31 Copyright © Houghton Mifflin Company. All rights reserved. 22

Theorem 1. 11 Properties of Continuity Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 1. 11 Properties of Continuity Copyright © Houghton Mifflin Company. All rights reserved. 23

Theorem 1. 12 Continuity of a Composite Function Copyright © Houghton Mifflin Company. All

Theorem 1. 12 Continuity of a Composite Function Copyright © Houghton Mifflin Company. All rights reserved. 24

Theorem 1. 13 Intermediate Value Theorem Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 1. 13 Intermediate Value Theorem Copyright © Houghton Mifflin Company. All rights reserved. 25

Figure 1. 35 and Figure 1. 36 Copyright © Houghton Mifflin Company. All rights

Figure 1. 35 and Figure 1. 36 Copyright © Houghton Mifflin Company. All rights reserved. 26

Definition of Infinite Limits and Figure 1. 40 Copyright © Houghton Mifflin Company. All

Definition of Infinite Limits and Figure 1. 40 Copyright © Houghton Mifflin Company. All rights reserved. 27

Definition of Vertical Asymptote Copyright © Houghton Mifflin Company. All rights reserved. 28

Definition of Vertical Asymptote Copyright © Houghton Mifflin Company. All rights reserved. 28

Theorem 1. 14 Vertical Asymptotes Copyright © Houghton Mifflin Company. All rights reserved. 29

Theorem 1. 14 Vertical Asymptotes Copyright © Houghton Mifflin Company. All rights reserved. 29

Theorem 1. 15 Properties of Infinite Limits Copyright © Houghton Mifflin Company. All rights

Theorem 1. 15 Properties of Infinite Limits Copyright © Houghton Mifflin Company. All rights reserved. 30

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