证明当x→0时,e^x-1与x是等价无穷小

2025-06-22 13:58:36
推荐回答(1个)
回答1:

令:t = e^x -1 , x = ln(1+t) , x->0, t->0

lim(x->0) [e^x - 1]/x
=lim(t->0) t/ln(1+t)
=lim(t->0) 1/[ln(1+t)^(1/t)]
= 1/lne
= 1