作业帮极限为什么等于0?
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/20 09:38:07
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极限为什么等于0?
极限为什么等于0?
极限为什么等于0?
=[x→1]lim{[(1-x)/x]ln(1-x)}
=[x→1]lim{ln(1-x)/[x/(1-x)]}
=[x→1]lim{-(1-x)/[(1/(1-x)+x*(-1)/(1-x)²]}
=[x→1]lim{-(1-x)/[(1-2x)/(1-x)²]}
=[x→1]lim{-(1-x)/(1-2x)}
=-(1-1)/(1-2*1)
=0
将x=1带入就等于0啊1-x趋于正0,1-x的对数趋于无穷大。无穷大乘0不是未定式么。你这么说不妥吧。原式=lim(x-->1-0)ln(1-x)/[x/(1-x)]
=lim(x-->1-0)[-1/(1-x)]/[(1-x+x)/(1-x)^2]
=lim(x-->1-0)[-(1-x)]
=0