括号里的极限为什么区域1谢谢

2025-06-25 17:06:51
推荐回答(2个)
回答1:

因为当x趋近于0时,x和arctanx是等价无穷小

回答2:

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)