If $f(x)= \begin{cases}\frac{\sin [x]}{[x]} & \text { for }[x] \neq 0 \\ 0 & \text { for }[x]=0\end{cases}$ where, $[x]$ denotes the greatest integer less than or equal to $x$, then $\lim _{x \rightarrow 0} f(x)$ is equal to

• A

  $1$
• B

  $-1$
• C

  $0$
• Correct answer
  D

  Does not exist

Solution

Hence, limit does not exist.

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