求极限！！！ limx→1ˉ(1-x)In(1-x) limx→1{1/(x-1)-1/Inx}

limx→1ˉ(1-x)In(1-x)
=limx→1ˉIn(1-x)/[1/(1-x)]
使用洛必达法则
=limx→1ˉ1/(1-x)/[1/(1-x)^2]
=limx→1ˉ(1-x)
=0

limx→1{1/(x-1)-1/Inx}
=limx→1{[lnx-(x-1)]/[（x-1)Inx]}
洛必达法则
=limx→1{[1/x-1)]/[Inx+(x-1)/x]}
=limx→1{(1-x)/[xInx+(x-1)]}
洛必达法则
=limx→1{-1/(1+lnx+1)}
=limx→1{-1/(2+lnx)}
=-1/2

limx→1ˉ(1-x)In(1-x)=limx→1ˉln(1-x)/[1/(1-x)](使用罗必塔法则)
=limx→1ˉ[-1/(1-x)]/[1/(1-x)^2]=limx→1ˉ(x-1)=0ˉ.
limx→1{1/(x-1)-1/Inx}=limx→1{[lnx-(x-1)]/[(x-1)lnx]}(使用罗必塔法则)
=limx→1{(1/x-1)/[1-1/x+lnx]}=limx→1{(-1/x^2)/(1/x^2+1/x)}
=limx→1{1/(x+1)}=1/2.