A) 0
B) \[\frac{2}{9}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{3}\]
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{\sin \sqrt{t}}}{{{x}^{3}}}dt=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x.2x}{3{{x}^{2}}}\] \[=\frac{2}{3}\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x}{x}\] (using Leibnitz's rule) \[=\frac{2}{3}.1=\frac{2}{3}\]You need to login to perform this action.
You will be redirected in
3 sec