求lim(x->+∞)[(1+1/x)^(x^2)-e^x]/x

Question

帮帮忙，求lim(x->+∞)[(1+1/x)^(x^2)-e^x]/x，答案是-e/2

Answer 1

=lim(e^(x²ln(1+1/x))-e^x)/x
=lime^x(e^(x²ln(1+1/x)-x)-1)/x
=lim(x²ln(1+1/x)-x)/xe^(-x)
=lim(xln(1+1/x)-1)/e^(-x)
=lim(ln(1+1/x)+x(-1/x²)/(1+1/x))/-e^(-x)
=lim(ln(1+1/x)-1/(1+x))/-e^(-x)
=lim(-1/x(1+x)+1/(1+x)²)/e^(-x)
=lim-e^x/x(1+x)²
=-∞本回答被网友采纳

Answer 2

楼主你算出来了吗，我也搞不对答案，好困扰啊