The function defined by    $f\left(x\right)=\left\{\begin{array}{l}x\sin \frac{1}{x}\text{ for }x\ne 0\\ \text{ 0 for }x=0\end{array}\right.$    at  $x=0$ is

• A

  continuous  
   

• B

  Discontinuous

• C

  Left continuous 

• D

  Right continuous