JEE Main Solved Paper 2017 Question 20
Question: $ \underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\cot x-\cos x}{{{(\pi -2x)}^{3}}} $ [JEE Main Solved Paper-2017]
Options:
A) $ \frac{1}{4} $
B) $ \frac{1}{24} $
C) $ \frac{1}{16} $
D) $ \frac{1}{8} $
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Answer:
Correct Answer: C
Solution:
$ \underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\cot x(1-\sin x)}{-8{{( x-\frac{\pi }{2} )}^{3}}} $
$ =\underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\tan ( \frac{\pi }{2}-x )}{8( \frac{\pi }{2}-x )}\frac{( 1-\cos ( \frac{\pi }{2}-x ) )}{{{( \frac{\pi }{2}-x )}^{2}}} $ $ =\frac{1}{8}.1.\frac{1}{2}=\frac{1}{16} $
