求这道题的解题过程
发布网友
发布时间：2023-11-07 20:40
共1个回答
热心网友
时间：2024-12-02 14:24
x->0
ln(1+x) = x -(1/2)x^2 +o(x^2)
ln(1+x)/x = 1-(1/2)x +o(x)
1/L
=lim(x->0) [ ln(1+x)/x ]^(1/x)
=lim(x->0) [ 1- (1/2)x ]^(1/x)
=e^(-1/2)
=> L = e^(1/2)
lim(x->0) [ x/ln(1+x) ]^(1/x) = e^(1/2)
