设f'(a)=a^2,且b>a>0,求f(b)-f(a)/lnb-lna在b趋向于a时的极值.

lim(b→a)（f(b)-f(a)）/（lnb-lna）=lim(b→a)[（f(b)-f(a)）/(b-a)]（b-a）/ln(b/a)
=lim(b→a)（f(b)-f(a)）/(b-a)*lim(b→a)（b-a）/ln(b/a)
=lim(s→a)f'(s)*lim(b→a) (b-a）/ln(1+(b-a)/a)
=lim(s→a)f'(s)*lim(b→a)a[(b-a)/a]/ln(1+(b-a)/a)
=a² a=a^3