计算下列极限：
(1) $\lim _{x \rightarrow 0}(1-x)^{\frac{1}{x}}$;
(2) $\lim _{x \rightarrow 0}(1+2 x)^{\frac{1}{x}}$;
(3) $\lim _{x \rightarrow \infty}\left(\frac{1+x}{x}\right)^{2 x}$;
(4) $\lim _{x \rightarrow \infty}\left(1-\frac{1}{x}\right)^{k x}$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$