limx趋向0 (e^x+x)^1/x

问题描述:

limx趋向0 (e^x+x)^1/x

L=lim(x->0) (e^x+x)^(1/x)
lnL =lim(x->0) ln(e^x+x) /x (0/0)
= lim(x->0)(e^x+1)/(e^x+x)
=2
L= e^2