Functions Question 78
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{x\cos x-\sin x}{x^{2}\sin x}= $
[MNR 1984,86]
Options:
A) $ \frac{1}{3} $
B) $ -\frac{1}{3} $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{x\cos x-\sin x}{x^{2}\sin x} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{-\sin x}{2\sin x+x\cos x} $ (By L-Hospital?s rule) $ =\underset{x\to 0}{\mathop{\lim }},\frac{-\cos x}{3\cos x-x\sin x}=-\frac{1}{3} $ , (Again by L-Hospital?s rule)
BETA
