limx趋向0 (e-(1+x)^1/x )/x 求极限
问题描述：
limx趋向0 (e-(1+x)^1/x )/x 求极限
答
lim(x->0)(exp(1)-(1+x)^(1/x))/x =lim(x->0)(exp(1)-exp(1)exp(ln(1+x)/x-1))/x =lim(x->0)exp(1)(1-exp(ln(x+1)/x-1))/x 利用等价无穷小 =lim(x->0)exp(1)(-(ln(x+1)/x-1))/x =lim(x->0)exp(1)...