If the function $f\left(x\right)$ defined by $f\left(x\right)=\left\{\begin{array}{ccc}x\sin \frac{1}{x} & \mathrm{f}\mathrm{o}\mathrm{r}& x\ne 0\\ k& \mathrm{f}\mathrm{o}\mathrm{r}& x=0\end{array}\right.$ is continuous at $x=0$ , then $k=$ _______

• Correct answer
  A

  $0$
• B

  $1$
• C

  $-1$
• D

  $\frac{1}{2}$

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