A) ½
B) 0
C) 1
D) None of these
Correct Answer: A
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{x\cos x-\log (1+x)}{{{x}^{2}}}\], \[\left( \frac{0}{0}\text{form} \right)\] Applying L-Hospital?s rule, we have \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\cos x-x\sin x-\frac{1}{x+1}}{2x}\], \[\left( \frac{0}{0}\text{form} \right)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{-\sin x-\sin x-x\cos x+\frac{1}{{{(x+1)}^{2}}}}{2}=\frac{1}{2}\].
You need to login to perform this action.
You will be redirected in
3 sec
