Evaluate the given limit: mathop {lim }limits | vedclass

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(A) We are given the limit: $\mathop {\lim }\limits_{x 	o \pi } \frac{\sin (\pi-x)}{\pi(\pi-x)}$Let $y = \pi - x$. As $x 	o \pi$,$y 	o 0$.Substitut

Vedclass · Accepted Answer

$\frac{1}{\pi}$

Vedclass · Answer

(A) We are given the limit: $\mathop {\lim }\limits_{x 	o \pi } \frac{\sin (\pi-x)}{\pi(\pi-x)}$Let $y = \pi - x$. As $x 	o \pi$,$y 	o 0$.Substituting this into the limit,we get:$\mathop {\lim }\limits_{y 	o 0} \frac{\sin y}{\pi y}$$= \frac{1}{\pi} \mathop {\lim }\limits_{y 	o 0} \frac{\sin y}{y}$Using the standard limit formula $\mathop {\lim }\limits_{y 	o 0} \frac{\sin y}{y} = 1$,we have:$= \frac{1}{\pi} 	imes 1 = \frac{1}{\pi}$

Evaluate the given limit: $\mathop {\lim }\limits_{x \to \pi } \frac{\sin (\pi-x)}{\pi(\pi-x)}$

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