limx→∞(x+3/x-2)^x求极限
问题描述：
limx→∞(x+3/x-2)^x求极限
limx→∞(x+3/x-2)^x 求极限
答
lim(x->∞) [(x+3)/(x-2)]^x
=lim(x->∞) [1 + 5/(x-2)]^x
=e^lim(x->∞) [ 5x/(x-2)]
=e^lim(x->∞) [ 5/(1-2/x)]=e^5