Answer
$\underset{x\to -3}{\mathop{\lim }}\,\left( 4-{{x}^{2}} \right)=-5$, because as x-approaches $-3$, the value of $ f\left( x \right)$ gets closer to $-5$.
Work Step by Step
Consider the provided function, $ f\left( x \right)=4-{{x}^{2}}$.
To plot the graph of the function $ y=4-{{x}^{2}}$ substitute different values of x in the equation $ y=4-{{x}^{2}}$ to get different values of y.
Now, consider the provided limit, $\underset{x\to -3}{\mathop{\lim }}\,\left( 4-{{x}^{2}} \right)$.
Consider the obtained graph of $ f\left( x \right)=4-{{x}^{2}}$.
To find $\underset{x\to -3}{\mathop{\lim }}\,\left( 4-{{x}^{2}} \right)$, examine the portion of the graph near $ x=-3$.
As x gets closer to $-3$, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $-5$. This point $\left( -3,-5 \right)$ is as shown in the above graph.
The point $\left( -3,-5 \right)$ has a y-coordinate of $-5$.
Thus, $\underset{x\to -3}{\mathop{\lim }}\,\left( 4-{{x}^{2}} \right)=-5$.
Hence the value of $\underset{x\to -3}{\mathop{\lim }}\,\left( 4-{{x}^{2}} \right)$ is $-5$.
