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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} $

1 Answer

$ \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)}$
$ = \large\frac{1}{\pi} \quad$ Using $\bigg[ \lim\limits_{y \to 0} \large\frac{ \sin \: y}{y} $$ = 1 \bigg]$
answered Apr 4, 2014 by thanvigandhi_1
edited May 16, 2014 by balaji.thirumalai
 

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