若 $\lim _{x \rightarrow 0} \frac{\cos \left(x e^x\right)-e^{-\frac{x^2}{2} e^{2 x}}}{x^\alpha}=\beta \neq 0$ 则
$\text{A.}$ $\alpha=2, \beta=-1$.
$\text{B.}$ $\alpha=3, \beta=-\frac{1}{6}$.
$\text{C.}$ $\alpha=4, \beta=-\frac{1}{12}$.
$\text{D.}$ $\alpha=5, \beta=-\frac{1}{8}$.