极限计算问题lim x→∞ [(x-1)/(x+3)]^(x+1)
问题描述：
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)
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)