设f导数(x0)存在且等于4,则lim(x趋向于x0) x除以[f（x0-2x)-f(x0-x)]=__?

Lim (x->0) [ f(x0-2x) - f(x0) ] / x
= (-2) Lim (x->0) [ f(x0-2x) - f(x0) ] / (-2x)
= (-2) Lim (u->0) [ f(x0+u) - f(x0) ] / u 令 u = -2x
= - 2 f '(x0)
同理 Lim (x->0) [ f(x0) - f(x0-x) ] / x = f '(x0)
于是 Lim (x->0) [ f(x0-2x) - f(x0-x) ] / x
= Lim (x->0) [ f(x0-2x) - f(x0) + f(x0) - f(x0-x) ] / x
= Lim (x->0) [ f(x0-2x) - f(x0) ] / x + Lim(x->0) [ f(x0) - f(x0-x) ] / x
= - f '(x0) = - 4
故 Lim (x->0) x /[ f(x0-2x) - f(x0-x) ] = - (1/4)