Browse Questions

# Evaluate the following limits  $\lim\limits_{ x \to \pi} \large\frac{ \sin ( \pi - x)}{ \pi ( \pi - x)}$

$\begin{array}{1 1} \large\frac{1}{\pi} \\ \pi \\ -\large\frac{1}{\pi} \\-\pi \end{array}$

$\lim\limits_{ x \to \pi} \large\frac{ \sin ( \pi - x)}{ \pi ( \pi - x)}$
We can see that when $x \to n \Rightarrow ( n - x) \to 0$.
$\Rightarrow \lim\limits_{ x \to \pi} \large\frac{ \sin ( \pi - x)}{ \pi ( \pi - x)}$$= \large\frac{1}{\pi}$$ \; \lim\limits_{(\pi - x) \to 0} \large\frac{\sin ( \pi-x)}{ (\pi - x)}$