设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
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设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt,则F′﹙0﹚=_______设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2,令F﹙x﹚=∫﹙0,
设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
lim(x→0) ƒ(x)/x = 2
F(x) = ∫(0→1) ƒ(xt) dt
令u = xt,du = x dt
t = 0,u = 0
t = 1,u = x
F(x) = ∫(0→x) ƒ(u) * (1/x du)
F(x) = (1/x)∫(0→x) ƒ(u) du
F'(x) = (1/x)ƒ(x) - (1/x²)∫(0→x) ƒ(u) du
F'(0) = lim(x→0) ƒ(x)/x - lim(x→0) [∫(0→x) ƒ(u) du]/x²
= 2 - lim(x→0) ƒ(x)/(2x)
= 2 - (1/2)(2)
= 1
设f(x)为连续函数,且满足f(x)=1+[(1-x^2)^1/2]*∫﹙0→1﹚f(x)dx,求f(x)
设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______谢谢!
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