![[Love]](/static/emoticons/Love.png)
我闲的蛋疼
lim(x→0+)x^x
=lim(x→0+)e^x·lnx
<=>lim(x→+∞)e^(-ln(x)/x)
=1
lim(x→0+)lnx·ln(1-x)
<=>lim(x→+∞)-lnx·[ln(x-1)-lnx]
=lim(x→+∞)(lnx)^2-lnx·ln(x-1)
=lim(x→+∞)[(lnx·lnx)^2-[lnx·ln(x-1)]^2]/[(lnx)^2+lnx·ln(x-1)]
=lim(x→+∞)[(lnx)^2-[ln(x-1)]^2]/[1+ln(x-1)/lnx]
=0