If $f\left(x\right)=\left\{\begin{array}{cc}{x}^{\alpha }\cos (1/x),& ifx\ne 0\\ 0,& ifx=0\end{array}\right.\begin{array}{} \\ \end{array}$ is continuous at x = $a$ then 

• A

  $\alpha <0$

• B

  $\alpha >0$

• C

  $\alpha =0$

• D

  $\alpha \ge 0$