作业帮极限计算问题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)
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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)
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)
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)
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)
lim x→∞ [(x-1)/(x+3)]^(x+1)
=lim x→∞ [1-4/(x+3)]^{[-(x+3)/4]*(-4)(x+1)/(x+3)} （分离e。对于一般的指数函数求极限，在无法用洛必达法则求导得值时，首先分离e）
=e^{lim x→∞ -4(x+1)/(x+3)}
=e^(-4)
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