若lim(h趋于0)[f(0)-f(2h)]/h=1/2 则f'(0)=?

问题描述:

若lim(h趋于0)[f(0)-f(2h)]/h=1/2 则f'(0)=?

lim(h趋于0)[f(0)-f(2h)]/h
=lim(h趋于0)[f(0)-f(2h)]/2h *2
=lim(h趋于0)[f(0)-f(2h)]/(-2h) *(-2)
=f'(0)*(-2)=1/2
则f'(0)=-1/4