Question: Find the following limits

(a) \(\underset{x\to 4}{\mathop{\lim }}\,\frac{\frac{1}{\sqrt{x}}-\frac{1}{2}}{x-4}\)

(b) \(\underset{x\to 2}{\mathop{\lim }}\,f\left( x \right)\)

where \(f\left( x \right)=\left\{ \begin{aligned} & 1+2x\,\,\,\,\,\,\,\,x\le 2 \\ & {{x}^{2}}+2\,\,\,\,\,\,\,\,x>2 \\ \end{aligned} \right.\)