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Chapter 1: Q. 33 (page 88)

Consider the graph of the function:

Find the limits of function.

Short Answer

Expert verified

The limit of the function is 2.

Step by step solution

01

Step 1. Given graph

02

Step 2. Finding limits to the left 

Herethelimitexpressionis:limx->2-f(x)Fromthegraph,thefunctionalvaluetotheleftofx=2Isf(x)=-2Therefore,limx->2-f(x)=-2.

03

Step 3. Finding limits to the right

Herethelimitexpressionis:limx->2-f(x)Fromthegraph,thefunctionalvaluetotheleftofx=2Isf(x)=2Therefore,limx->2-f(x)=2.

04

Step 4.Finding limits to the points

Herethelimitexpressionis:limx->2-f(x)Fromthegraph,therearetwofunctionalatthepointx=2buttheyareforleftorrightlimitsThereisnofunctionalvalueatx=2Therefore,limx->2-f(x)=NovalueHencethelimitofthefunctionisf(2)=2.

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Most popular questions from this chapter

In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

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