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设f(x)在[0,1]上连续且递减,试证:当0<λ<1时,.
设f(x)在[0,1]上连续且递减,试证:当0<λ<1时,.
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设f(x)在[0,1]上连续且递减,试证:当0<λ<1时,.
设f(x)在[0,1]上连续且f(x)≥a>0,
试证 ∫01Inf(x)dx≤Inf∫01f(x)dx.
设f(x)在[0,1]上连续且单调减,试证对任何a∈(0,1)有
∫0af(x)dx≥a∫01f(x)dx
设函数f(x)在区间[0,1]上连续,在(0,1)内可导,且满足条件试证:存在ξ∈(0,1),使f(ξ)+ξf'(ξ)=0
设f(x)在闭区间[0,1]上连续,在开区间(0,1)内可导,且f(0)=f(1)=0,试证在(0,1)内至少存在一点ξ使得f′(ξ)= -(1/ξ)f(ξ)(ξ∈0,1)
设f(x)在[0,1]上连续,在(0,1)内可导,且f(0)=f(1)=0,试证在(0,1)内至少存在一点c,使
设f(x)在区间[0,1]上连续,在(0,1)内可导,且满足,试证存在一点ξ∈(0,1),使f(ξ)+ξf'(ξ)=0
设f(x)在[0,1]上连续,在(0,1)内可导,且f(0)=0,试证在(0,1)内至少存在一点c,使
cf'(c)+kf(c)=f'(c)
设f(x)在[0,1]上连续,且∫01f(x)dx=0,∫01xf(x)dx=0,…,∫01xn-1f(x)dx=0,而∫01xnf(x)dx=1,试证在[0,1]上至少存在一点x0,使得|f(x0)|≥2n(n+1).