Question

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

Answer 1

$\begin{array}{c}{lim}_{x\to a}\frac{\sin x-\sin a}{\left(x-a\right)}\\ Itis\frac{0}{0}form,thenuse{L}_{1}Hospitalrule\\ \Rightarrow {lim}_{x\to a}\frac{\cos x-0}{1}\\ \Rightarrow {lim}_{x\to a}\cos a=\cos aAns.\end{array}$