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设f(x)在x=0处可导,则lim(h趋于0)(f(3h)-f(-h))/2h=?
人气:336 ℃ 时间:2019-08-18 09:27:38
解答
[f(0+3h)-f(0)+f(0)-f(0-h)]/2h
=[f(0+3h)-f(0)]/2h+[(f(0)-f(0-h)]/2h
由导数定义可知lim(h趋于0)[f(0+3h)-f(0)]/2h=(3/2)f'(0)
lim(h趋于0)[(f(0)-f(0-h)]/2h=(1/2)f'(0)
于是原式=2f'(0)
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