Question

Evaluate the following limits.
$\underset{x\to a}{lim}\frac{\sin \sqrt{x}-\sin \sqrt{a}}{x-a}$.

Answer 1

$\begin{array}{c}{lim}_{x\to a}\frac{\sin \sqrt{x}-\sin \sqrt{a}}{\left(x-a\right)}\\ Itis\frac{0}{0}form\\ use{L}_{1}HospitalRule\\ \Rightarrow {lim}_{n\to a}\cos \sqrt{x}.\frac{1}{2\sqrt{x}}-0\\ \Rightarrow {lim}_{n\to a}\frac{1}{2\sqrt{a}}\cos \sqrt{a}Ans.\end{array}$