   Chapter 2, Problem 2RCC

Chapter
Section
Textbook Problem

Describe several ways in which a limit can fail to exist illustrate with sketches.

To determine

To describe: The limit can fail to exist in several ways.

Explanation

The limit fails to exist for several ways are:

1. (i) The left and right limits are not equal

Graph:

Example: limx3f(x)

Here f(x) approaches to two different values depending on direction of x approaches from. In graph limx3f(x)2 and limx3+f(x)3.

(ii) When the function approach a infinity large value the limit fails to exits.

Graph:

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