x→无穷大,求（x+1)/(x-2)的x次方的极限,是否为e的3次方_数学解答

x→无穷大,求（x+1)/(x-2)的x次方的极限,是否为e的3次方

人气：415 ℃　时间：2020-09-21 14:51:34

解答

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