Q235 / 270 · NDA 2012 (Phase 1) · Mathematics

What is $\lim _{x \rightarrow 0} x^2 \sin \left(\frac{1}{x}\right)$ equal to?

  • Correct answer
    A
    0
  • B
    1
  • C
    1/2
  • D
    Limit does not exist

Solution

$\lim _{x \rightarrow 0}\left(x^2\right)\left[\sin \left(\frac{1}{x}\right)\right]$ since $\sin \frac{1}{x}$ is odd and $x^2$ approaches to zero $=0$.

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

More Limits Questions