Q100 / 160 · TS EAMCET 2005 · Mathematics

$\lim _{x \rightarrow 0} x^2 \sin \frac{\pi}{x}$ is equal to

  • A
    1
  • Correct answer
    B
    0
  • C
    does not exist
  • D
    $\infty$

Solution

$\begin{aligned} & \lim _{x \rightarrow 0} x^2 \sin \left(\frac{\pi}{x}\right) \\ &=\lim _{x \rightarrow 0} \pi x \cdot \frac{\sin \frac{\pi}{x}}{\frac{\pi}{x}}=0(1)=0\end{aligned}$

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

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