已知f(3)=2 f‘(3)=-2则lim(x→3)[2x-3f(x)]/(x-3)的值为
问题描述:
已知f(3)=2 f‘(3)=-2则lim(x→3)[2x-3f(x)]/(x-3)的值为
答
lim(x->3) [2x-3f(x)]/(x-3)
=-lim(x->3) [3f(x)-2x]/(x-3)
=-lim(x->3) [3f(x)-6-2x+6]/(x-3)
=-3*lim(x->3) [f(x)-f(3)]/(x-3) +2
=-3f'(3)+2
=-3*(-2)+2
=8