极限计算问题lim x→∞ [(x-1)/(x+3)]^(x+1)lim x→∞ [(x-1)/(x+3)]^(x+1)我只知道答_数学解答

极限计算问题lim x→∞ [(x-1)/(x+3)]^(x+1)
lim x→∞ [(x-1)/(x+3)]^(x+1)
我只知道答案是e^(-4)

人气：238 ℃　时间：2020-01-27 14:00:44

解答

lim x→∞ [(x-1)/(x+3)]^(x+1)
=lim x→∞ [1-4/(x+3)]^(x+1)
=lim x→∞ [1-4/(x+3)]^{[-(x+3)/4]*(-4)(x+1)/(x+3)}
=e^{lim x→∞ -4(x+1)/(x+3)}
=e^(-4)