A) \[1\]
B) \[\infty \]
C) \[\frac{2}{\pi }\]
D) 0
Correct Answer: C
Solution :
\[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \frac{\pi x}{2}\] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{(1-x)}{\cot \frac{\pi x}{2}}\] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{-1}{-\frac{\pi }{2}\cos e{{c}^{2}}\frac{\pi x}{2}}\] [By L Hospital rule] \[=\frac{2}{\pi }\]
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