## Precalculus (6th Edition) Blitzer

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