计算下列极限.
(1) $\lim _{x \rightarrow 0} \dfrac {(1+2x)^{ \sin x}-1}{x^{2}}$.
(2)$ \lim _ {x \rightarrow 0} \dfrac { \ln (e+ \sin 2x)-1}{x}$.
(3) $\lim _ {x \rightarrow 0} \dfrac { \ln \frac { \sin x}{x}}{ \tan ^{2}x}$.
(4)$ \lim _ {x \rightarrow 0} \dfrac {e^{ \tan x}-e^{x}}{x^{3}}$.
(5) $\lim _ {x \rightarrow 0} \dfrac { \sqrt {1+x \cos x}- \sqrt {1+x}}{x^{2} \arcsin 2x}$.
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$