limx→0+ tanx•lnx=limx→0+ tanx1lnx=limx→0+1cos2x-1ln2x•1x=-limx→0+xln2xcos2x=-limx→0+ln2x1x=-limx→0+1x2lnx-1x2=limx→0+2lnx1x=limx→0+2x-1x2=limx→0+（-2x）=0．
