设函数 $f(x)=\iint_{u^2+v^2 \leqslant x^2} \arctan \left(1+\sqrt{u^2+v^2}\right) \mathrm{d} u \mathrm{~d} v(x>0)$, 则 $\lim _{x \rightarrow 0^{+}} \frac{f(x)}{\mathrm{e}^{-2 x}-1+2 x}=$
A
$-\frac{\pi^2}{8}$.
B
$-\frac{\pi^2}{4}$.
C
$\frac{\pi^2}{4}$.
D
$\frac{\pi^2}{8}$.
E
F