A) 2
B) 1
C) 0
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{{{\cos }^{2}}t\,\,dt}}{x\sin x}\] Using L Hospitals rule, we get \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\cos }^{2}}({{x}^{2}})\cdot 2x-0}{x\cos x+\sin x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2{{\cos }^{2}}({{x}^{2}})}{\cos x+\frac{\sin x}{x}}\] \[=\frac{2}{2}=1\]
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