Question

证明当x→0时,e^x-1与x是等价无穷小 ,急求答案,要过程,跪求…大虾帮帮忙

Answer 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