F(x)=∫[0,x] (x^2-t^2)f(t)dt
=x^2 ∫[0,x]f(t)dt - ∫[0,x] t^2 f(t)dt
F'(x)=2x ∫[0,x]f(t)dt + x^2 f(x) - x^2 f(x)=2x ∫[0,x]f(t)dt
lim[x->0] F'(x)/x^k = 2x ∫[0,x]f(t)dt/x^k
=2lim[x->0] ∫[0,x]f(t)dt/x^(k-1) 0/0,洛必达
=2lim[x->0] f(x)/(k-1)x^(k-2) 0/0,洛必达
=2lim[x->0] f'(x)/(k-1)(k-2)x^(k-3) 分子不为0,同阶无穷小,所以分母不为0,所以k-3=0,k=3可以,因为是->0(趋近于0),而不是等于0,所以可以约掉 lim[x->0] F'(x)/x^k = lim[x->0] 2x ∫[0,x]f(t)dt/x^k这边写的急了,漏了个极限lim(x→0)x^2/x=lim(x→0) x = 0