$\text{ If }f\left(x\right)=\left\{\begin{array}{cl}{x}^{\alpha }\cos \left(\frac{1}{x}\right)& ,\text{ if }x\ne 0\\ 0,& \text{ if }x=0\end{array}\text{ is continuous at }x=0\right.\text{ then }$

• A

  $\alpha <0$

• B

  $\alpha >0$

• C

  $\alpha =0$

• D

  $\alpha \ge 0$