Q115 / 160 · WBJEE 2011 · Mathematics

\(\lim _{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\)

  • A
    \(\pi^2\)
  • B
    \(3 \pi\)
  • C
    \(2 \pi\)
  • Correct answer
    D
    \(\pi\)

Solution

\(\begin{aligned} & \text {Hints : }=\operatorname{Lt}_{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\pi_{x \rightarrow 0} \frac{\sin ^2 x}{x^2}=\pi \\ & =\pi \end{aligned}\)

Hence, the correct answer is option: 'D'.

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