若x→0时,F(x)=
(x
2-t
2)f′(t)dt的导数与x
2为等价无穷小,则f′(0)=______.
人气:123 ℃ 时间:2019-11-25 14:13:33
解答
F(x)=∫x0x2f′(t)dt−∫x0t2f′(t)dt,求导得,F′(x)=2x∫x0f′(t)dt+x2f′(x)−x2f′(x)=2x∫x0f′(t)dt,又x→0时,F(x)=∫x0(x2-t2)f′(t)dt的导数与x2为等价无穷小,所以1=limx→02x∫x0f′(t)dtx2=l...
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