当x-->1时,lnx=ln(1+x-1)与x-1等价,所以利用等价无穷小的替换得lim(x-->1)[x/(x-1)] /(1/lnx)=lim(x-->1)(xlnx)/(x-1) =lim(x-->1)(x(x-1))/(x-1) =lim(x-->1)x=1.
