下列各式正确的是:
$\text{A.}$ $\lim _{x \rightarrow+\infty} \frac{\sin x}{x}=1$
$\text{B.}$ $\lim _{x \rightarrow 0} \frac{\sin x}{x}=0$
$\text{C.}$ $\lim _{x \rightarrow+\infty}\left(1+\frac{1}{x}\right)^x=-e$
$\text{D.}$ $\lim _{x \rightarrow-\infty}\left(1+\frac{1}{x}\right)^x=e$