Question

求极限，题目如下：

第一步是怎么来的？

Answer 1

x->0
arctanx = x-(1/3)x^3 +o(x^3)
arctanx/x = 1-(1/3)x^2 +o(x^2)
//
lim(x->0) (arctanx/x)^(1/x^2)
=lim(x->0) [1-(1/3)x^2]^(1/x^2)
=e^(-1/3)