当 $x \rightarrow+\infty$ 时, $f(x)=\left(x^3-x^2+\frac{1}{2} x\right) \mathrm{e}^{\frac{1}{x}}-\sqrt{x^6+1}-\frac{1}{6}$ 是 $g(x)=\alpha x^\beta$ 等价无穷小, 则 $\alpha, \beta=$
A. $\alpha=\frac{1}{2}, \beta=-1$
B. $\alpha=\frac{1}{8}, \beta=-1$
C. $\alpha=\frac{1}{8}, \beta=-2$
D. $\alpha=\frac{1}{2}, \beta=-2$