若f′(x0)=-2,则lim[f(x0+h)-f(x0-h)]/h=

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

若f′(x0)=-2,则lim[f(x0+h)-f(x0-h)]/h=
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.

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。