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Evaluate \mathrm{\lim _{x \rightarrow \pi} \frac{\pi-x}{\sin (x)}}

Option: 1

0

 


Option: 2

1


Option: 3

5


Option: 4

2


Answers (1)

best_answer

\begin{aligned} \mathrm{\lim _{x \rightarrow \pi} \frac{\pi-x}{\sin x} }& = \mathrm{-\frac{1}{\lim _{x \rightarrow \pi} \frac{\sin (x)-\sin (\pi)}{x-\pi}}} \\ \\& =-\frac{1}{\sin ^{\prime}(\pi)} \\ \\& =1 \end{aligned}

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Rakesh

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