先证明极限存在.连续用两次洛必达法则就OK了.1/Inx - 1/(x-1) = ( x-1-ln(x) ) / ( x*ln(x) - ln(x) )x --> 1 时,是 0/0 型,分子分母求导数( x-1 ) / ( x-1+x*ln(x) )x --> 1 时,还是 0/0 型,再求导数1 / (1+1+ln(x)...