Question

solve it step by step.. ​

Answer 1

Step-by-step explanation:

We have,

$\lim_{ x\rarr \pi} \frac{ \sin(\pi - x) }{\pi(\pi - x)}$

$= \lim_{ (x - \pi)\rarr 0} \frac{ \sin \{- (x - \pi ) \} }{\pi \{ - (x - \pi ) \}}$

$= \lim_{ (x - \pi)\rarr 0} \frac{ - \sin (x - \pi )}{ - \pi (x - \pi ) }$

$= \lim_{ (x - \pi)\rarr 0} \frac{ \sin (x - \pi )}{ \pi (x - \pi ) }$

$= \frac{1}{\pi} \lim_{ (x - \pi)\rarr 0} \frac{ \sin (x - \pi )}{ (x - \pi ) }$

$= \frac{1}{\pi} \times 1$

$= \frac{1}{\pi}$