当x→0时,F(x)=∫0→x (x^2-t^2)f"(t)dt的导数F'(x)与x^2为等价无穷小,则f"(0)=

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当x→0时,F(x)=∫0→x (x^2-t^2)f"(t)dt的导数F'(x)与x^2为等价无穷小,则f"(0)=
当x→0时,F(x)=∫0→x (x^2-t^2)f"(t)dt的导数F'(x)与x^2为等价无穷小,则f"(0)=

当x→0时,F(x)=∫0→x (x^2-t^2)f"(t)dt的导数F'(x)与x^2为等价无穷小,则f"(0)=
F(x)=x^2∫(0→x)f''(t)dt-∫(0→x)t^2f''(t)dt
F'(x)=2x∫(0→x)f''(t)dt+x^2f''(x)-x^2f''(x)=2x∫(0→x)f''(t)dt
F'(x)/x^2=2∫(0→x)f''(t)dt/x=2f''(x)
所以lim(x→0)F'(x)/x^2=2f''(0)=1
f''(0)=1/2