若f′(x0)=-2,则lim[f(x0+h)-f(x0-h)]/h=_数学解答

若f′(x0)=-2,则lim[f(x0+h)-f(x0-h)]/h=

人气：363 ℃　时间：2019-08-22 11:13:45

解答

lim(h->0){[f(x0+h)-f(x0-h)]/h}
=lim(h->0){[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h}
=lim(h->0){[f(x0+h)-f(x0)]/h}+lim(h->0){[f(x0-h)-f(x0)]/(-h)}
=f'(x0)+f'(x0) (根据导数定义)
=2f'(x0)
=2*(-2) (∵f′(x0)=-2)
=-4.