数学试题讲解

计算下列极限.
(1)

lim_{x \to 0} \frac{(1 + 2 x)^{\sin x} - 1}{x^{2}}

.

(2)

lim_{x \to 0} \frac{\ln (e + \sin 2 x) - 1}{x}

.

(3)

lim_{x \to 0} \frac{\ln \frac{\sin x}{x}}{\tan^{2} x}

.

(4)

lim_{x \to 0} \frac{e^{\tan x} - e^{x}}{x^{3}}

.

(5)

lim_{x \to 0} \frac{\sqrt{1 + x \cos x} - \sqrt{1 + x}}{x^{2} \arcsin 2 x}