Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.1 - Finding Limits Using Tables and Graphs - Exercise Set - Page 1139: 36


$\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)=5$, because as x-approaches $-2$, the value of $ f\left( x \right)$ gets closer to 5.

Work Step by Step

Consider the provided function, $ f\left( x \right)=9-{{x}^{2}}$. To plot the graph of the function $ y=9-{{x}^{2}}$ substitute different values of x in the equation $ y=9-{{x}^{2}}$ to get different values of y. Consider the provided limit, $\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)$. Consider the obtained graph of the function $ f\left( x \right)=9-{{x}^{2}}$. To find $\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)$, examine the portion of the graph near $ x=-2$. As x gets closer to $-2$, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $5$. This point $\left( -2,5 \right)$ is as shown in the above graph. The point $\left( -2,5 \right)$ has a y-coordinate of $5$. Thus, $\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)=5$. Hence the value of $\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)$ is $5$.
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