Question

求函数f(x)=(e^x-1)/(x-1)x的间断点

Answer 1

f(x)=(e^x-1)/[(x-1)x]
(x-1)x =0
x=0 or 1
lim(x->0) (e^x-1)/[(x-1)x]
=lim(x->0) 1/(x-1)
=-1
x=0: 可去间断点
lim(x->1+) (e^x-1)/[(x-1)x] ->+无穷
x=1：无穷间断点