求 lim(x→∞)[1-(3/x)]^x的极限.
问题描述：
求 lim(x→∞)[1-(3/x)]^x的极限.
答
lim(x→∞)[1-(3/x)]^x
=lim(x→∞)e^{ln[1-(3/x)]^x}
=e^lim(x→∞)xln[1-(3/x)]
lim(x→∞)xln[1-(3/x)]
=lim(x→∞){ln[1-(3/x)]}/(1/x)
由洛比达法则
=lim(x→∞)[x/(x-3)]*(-3/-x^2)/[1/(-x^2)]
=lim(x→∞)[x/(x-3)])]*-3
=-3
所以lim(x→∞)[1-(3/x)]^x=e^lim(x→∞)xln[1-(3/x)]=e^（-3）
本来很简单的题.在电脑上写出来看起来很复杂.Orz
用笔照这过程写一遍应该知道了.