原式=lim(x→1)[xlnx-(x-1)]/[(x-1)lnx]
此时分子分母均趋向0,用罗比达法则求导
=lim(x→1)lnx/[lnx+(x-1)/x]
=lim(x→1)xlnx/(xlnx+x-1)
此时分子分母仍均趋向0,再用罗比达法则求导
=lim(x→1)(lnx+1)/(lnx+2)
=1/2
即原极限为1/2