Question

求极限在线等

Answer 1

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

追问

怎么判断的？

😭能不能写一下

追答

lim(x->1+) 1/ [ 1- e^(x/(x-1)) ] =0
分子 =1, 分母->-∞
//
x->1-
-x/(x-1) -> +∞
e^(-x/(x-1)) -> +∞
1/e^(-x/(x-1)) -> 0
lim(x->1-) 1/ [ 1- e^(x/(x-1)) ]
=lim(x->1-) 1/ [ 1- 1/e^(-x/(x-1)) ]
=1/(1-0)
=1