解答题
1.设f'(x)连续，f(0)=0，f'(0)≠0，F(x)=∫0xtf(t2-x2)dt，且当x→0时，F(x)～xn，求n及f'(0)．
【正确答案】F(x)=∫0xtf(t2-x2)dt=
∫0xf(t2-x2)d(t2-x2)
=
∫-x22f(u)du
=
∫0-x2f(u)du，
∫0xf(t2-x2)d(t2-x2)=
∫-x22f(u)du=
∫0-x2f(u)du，【答案解析】