求极限!limx→1ˉ(1-x)In(1-x) limx→1{1/(x-1)-1/Inx}
问题描述：
求极限!limx→1ˉ(1-x)In(1-x) limx→1{1/(x-1)-1/Inx}
答
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.
答
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)=0limx→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-...