f'(3)=-2,求lim[2x-3f(x)]/(x-3),注:x->3

问题描述:

f'(3)=-2,求lim[2x-3f(x)]/(x-3),注:x->3

lim[2x-3f(x)]/(x-3)=lim[6-3f(x)+2x-6]/(x-3)
=lim[6-3f(x)]/(x-3)+lim(2x-6)/(x-3)
1、求lim[6-3f(x)]/(x-3)=-3*lim[f(x)-2]/(x-3)
=-3*lim[f(x)-f(3)]/(x-3)=-3f'(3)=6;
2、求lim(2x-6)/(x-3)直接化简为2;
所以原式=6+2=8