Answer
$\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)=-3$, since, as x approaches 2, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $-3$.
Work Step by Step
Consider the provided limit $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$.
To find $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$, examine the portion of the graph near $ x=2$.
As x approaches 2, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $-3$. This point $\left( 2,-3 \right)$ is shown by the solid dot in the above graph.
The point $\left( 2,-3 \right)$ has a y-coordinate of $-3$.
Thus, $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)=-3$.
Hence, the value of $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$ is $-3$.
