Question: Let

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{\sqrt{4-x}}{x-4}\,\,\,\,\,\,\,\,\,\,\,\,x<0 \\ & -\frac{1}{\sqrt{x+4}}\,\,\,\,\,\,\,\,\,\,\,\,x>0 \\ \end{aligned} \right.\]

Find the following limits if they exist

(a) \(\underset{x\to \infty }{\mathop{\lim }}\,f\left( x \right)\)

(b) \(\underset{x\to -\infty }{\mathop{\lim }}\,f\left( x \right)\)

(c) \(\underset{x\to 0}{\mathop{\lim }}\,f\left( x \right)\)

(d) \(\underset{x\to -4}{\mathop{\lim }}\,f\left( x \right)\)

(e) \(\underset{x\to 4}{\mathop{\lim }}\,f\left( x \right)\)