已知f'(x)=-1,limh趋于0f(x-2h)-f(x-h)/h=

Question

已知f'(x)=-1,limh趋于0 【 f(x-2h)-f(x-h)】/h=

Answer 1

解
令-h=t 当h→0,t=-h→0
lim(h→0) (f(x-2h)-f(x-h))/h
= -lim(t→0) (f(x+2t-f(x+t))/t
=-lim(t→0) (f(x+2t-f(x+t)-f(x)+f(x))/t
=-lim(t→0) (f(x+2t-f(x)-(f(x+t)-f(x)))/t
=-2lim(2t→0)(f(x+2t-f(x))/2t+lim(t→0)((f(x+t)-f(x))/t
=-2f'(x)+f'(x)
=-2*(-1)-1
=1