limx趋向于1 [lnx*ln(x-1)]

原式= lim (x→1) [ ln (x-1) / (1 / ln x) ].
由洛必达法则,
原式= lim (x→1) { [ 1/(x-1) ] / [ -1 / x(ln x)^2 ] }
= - lim (x→1) [ x (ln x)^2 /(x-1) ]
= - lim (x→1) x *lim (x→1) [ (2 ln x /x) /1 ]
= -1 *0
=0.
= = = = = = = = =
以上计算可能有误.
用计算器近似计算,结果为0.