Answer
$\underset{x\to -2}{\mathop{\lim }}\,\left( 9-{{x}^{2}} \right)=5$, 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 $5$.
