A) \[3\pi /4\]
B) \[2\pi /3\]
C) \[2/\pi \]
D) \[\pi /4\]
Correct Answer: C
Solution :
The given limit can be rewritten as \[\underset{x\to 1}{\mathop{\lim }}\,\frac{(1-x)}{\cot \frac{\pi }{2}x}\left( \frac{0}{0} \right)\] Using L' Hospital's rule \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{-1}{\cos \text{e}{{\text{c}}^{2}}\left( \frac{\pi }{2}x \right)\frac{\pi }{2}}=\frac{2}{\pi }\]
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