Question

Evaluate the Given limit: $\underset{x\to \pi }{lim}\frac{\sin (\pi -x)}{\pi (\pi -x)}$

Answer 1

$\underset{x\to \pi }{lim}\frac{\sin (\pi -x)}{\pi (\pi -x)}=\frac{1}{\pi }\underset{(z-x)\to 0}{lim}\frac{\sin (\pi -x)}{(\pi -x)}$
= $\frac{1}{\pi }\times 1,$ $\because [\underset{y\to 0}{lim}\frac{\sin y}{y}=1]$
= $\frac{1}{\pi }$