若f(3)=2,f'(3)=-2,则lim(x→3) 2x-3f(x)/x-3=
问题描述:
若f(3)=2,f'(3)=-2,则lim(x→3) 2x-3f(x)/x-3=
答
f'(3)=-2=lim(x→3)(f(x)-f(3))/(x-3)=lim(x→3)(f(x)-2)/(x-3)
lim(x→3) 2x-3f(x)/x-3=lim(x→3)(2x-6+6-3f(x))/(x-3)
=lim(x→3)(2-3(f(x)-2)/(x-3))=2-3*(-2)=8