设f′(χ)连续,f(0)=0,f′(0)≠0,F(χ)=∫0χtf(t2-χ2)dt,且当χ→0时,F(χ)~χn,求n及f′(0).

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问题 设f′(χ)连续,f(0)=0,f′(0)≠0,F(χ)=∫0χtf(t2-χ2)dt,且当χ→0时,F(χ)~χn,求n及f′(0).

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答案[*] 则n-2=2,n=4,且 [*] 于是f′(0)=-4.

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