x→无穷大,求（x+1)/(x-2)的x次方的极限,是否为e的3次方
问题描述：
x→无穷大,求（x+1)/(x-2)的x次方的极限,是否为e的3次方
答
lim(x→∞) [(x+1)/(x-2)]^x
=lim(x→∞) [1+3/(x-2)]^x
=lim(x→∞) [1+3/(x-2)]^{[(x-2)/3]*[3x/(x-2)]}
=lim(x→∞) e^[3x/(x-2)]
=e³