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  • Choose the correct answer out of 4 options given against each Question 〖lim〗┬(x→π) sin⁡x/(x-π) is A. 1 B. 2 C. –1 D. –2

    

Choose the correct answer out of 4 options given against each Question
\mathop{\lim }_{x \rightarrow \pi }\frac{\sin x}{x- \pi } 
is
A. 1
B. 2
C. –1
D. –2

Answers (1)

\\ \mathop{\lim }_{x \rightarrow \pi }\frac{\sin x}{x- \pi }=\mathop{\lim }_{x \rightarrow \pi }\frac{\sin \left( \pi -x \right) }{- \left( \pi -x \right) }=-1~ \\ \\ \mathop{\lim }_{x \rightarrow 0}\frac{\sin x}{x}=1~~~ \\ \\ \pi -x \rightarrow 0~~~x \rightarrow \pi \\ \\

Hence, the answer is option C

 

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