Answer
The value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$ is $-1$.
Work Step by Step
Consider the function $ f\left( x \right)={{x}^{3}}-x+5$,
The function $ f\left( x \right)={{x}^{3}}-x+5$ is a polynomial.
Find the value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$,
$\begin{align}
& \underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)=\underset{x\to -2}{\mathop{\lim }}\,{{x}^{3}}-\underset{x\to -2}{\mathop{\lim }}\,x+5 \\
& ={{\left( -2 \right)}^{3}}-\left( -2 \right)+5 \\
& =-8+2+5 \\
& =-1
\end{align}$
Thus, the value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$ is $-1$
