x趋于无穷时,(x/(x+1))^x求极限
问题描述：
x趋于无穷时,(x/(x+1))^x求极限
答
原式=lim(x->∞) [1-1/(x+1)]^x
=lim(x->∞) {[1+1/(-x-1)]^(-x-1)}^(-1)*[1+1/(-x-1)]^(-1)
=1/e
答
lim(x/(x+1))^x
=lim1/【(x+1）/x)】^x
=lim1/(1+1/x))^x
=1/e