A) 0
B) 2/9
C) 1/3
D) 2/3
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\int_{0}^{{{x}^{2}}}{\sin \,\sqrt{t}}}{{{x}^{3}}}dt\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(isn\,x)\cdot 2x}{3{{x}^{2}}}\](by Leibnitz rule) \[=\frac{2}{3}\,\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin \,x}{x}=\frac{2}{3}\times 1=\frac{2}{3}\]You need to login to perform this action.
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