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Chapter 1: Q. 35 (page 88)

Consider the graph of the function:

Find the limits of function.

Short Answer

Expert verified

The limit is undefined.

Step by step solution

01

Step 1. Given graph

02

Step 2. Finding limits to the left x=-1 

Herethelimitexpressionis:limx->1-g(x)Fromthegraph,thefunctionalvaluetotheleftofx=-1isg(x)=鈭�Therefore,limx->1-g(x)=鈭�

03

Step 3. Finding limits to the right  x=-1  

Herethelimitexpressionis:limx->1+g(x)Fromthegraph,thefunctionalvaluetotheleftofx=-1isg(x)=-鈭�Therefore,limx->1+g(x)=-鈭�

04

Step 4. Finding limits to the point 

Herethelimitexpressionis:limx->1g(x)Fromthegraph,thefunctionalvaluetotheleftofx=-1isg(x)=novalueTherefore,limx->1g(x)=novaluehencethelimitisundefined

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Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

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