数学试题讲解

设函数

f (x) = \iint_{u^{2} + v^{2} ⩽ x^{2}} \arctan (1 + \sqrt{u^{2} + v^{2}}) d u d v (x > 0)

, 则

lim_{x \to 0^{+}} \frac{f (x)}{e^{- 2 x} - 1 + 2 x} =

- \frac{π^{2}}{8}

. B.

- \frac{π^{2}}{4}

. C.

\frac{π^{2}}{4}

. D.

\frac{π^{2}}{8}