question_answer

Directions: Question No. 94 are based on the following paragraph. If f(x) and g(x) be two function, such that f [a] = g [a] = 0 and f and g are both differentiable at everywhere in some neighborhood of point a except possibly a. The \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}=\underset{x\to a}{\mathop{\lim }}\,\frac{f'(x)}{g'(x)'}\] provided \[f'\,(a)\] and \[g'\,(a)\]are not both zero The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{\sin \sqrt{t}dt}}{{{x}^{3}}}\] is

A)  0                                            

B)  \[\frac{2}{9}\]

C)  \[\frac{1}{3}\]                                  

D)  \[\frac{2}{3}\]