lim(x->1)lnx*ln(x 1)等于多少是lim(x->1)ln(x)ln(x-1)_数学解答

lim(x->1)lnx*ln(x 1)等于多少
是lim(x->1)ln(x)ln(x-1)

人气：155 ℃　时间：2020-03-23 09:44:28

解答

lim(x->1)ln(x)ln(x-1)
=lim(x->1)ln(x-1)/[1/ln(x)]
=lim(x->1)ln(x-1)'/[1/ln(x)]'
=-lim(x->1)x*lnx*lnx/(x-1)
=-lim(x->1)[lnx*lnx]'/(x-1)'
=-lim(x->1)2*lnx/x=-2*ln1=0