数学试题讲解

2.计算下列极限.
(1)

lim_{x \to 0} (\cos x + x^{2})^{\frac{1}{x \ln (1 + x)}}

.

(2)

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

.

(3)

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

.

(4)

lim_{x \to 0} {(\frac{\arctan x}{x})}^{\frac{1}{x^{2}}}