A) \[\frac{1}{3}\]
B) \[-\frac{1}{3}\]
C) 1
D) None of these
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)
You need to login to perform this action.
You will be redirected in
3 sec
