lim（x/（x-1）—1/lnx）x趋于1的极限

用两次洛必达法则通分lim(x/(x-1) -1/lnx)= lim(xlnx -x +1)/(x-1)lnx =lim(1+lnx-1)/((x-1)/x+lnx) (一次洛必达)=lim(xlnx)/(x-1+xlnx) = lim(1+lnx)/(1+1+lnx) (二次洛必达)=lim(1+lnx)/(2+lnx) (x->1,lnx=0)=1/2