求(x→∞)lim(1+2/x)^x的极限,
问题描述：
求(x→∞)lim(1+2/x)^x的极限,
答
(x→∞)lim(1+2/x)^x
=lim(1+2/x)^[(x/2)*2]
=e^2
这里用到了一个公式 (x→∞)lim(1+1/x)^x=e
答
(x→∞)lim(1+2/x)^x
=(x→∞)lim[(1+(1/(x/2)))^(x/2)]^(2)
=[(x→∞)lim(1+(1/(x/2)))^(x/2)]^(2)
=e^2