设f(x)在[0,π]上连续,(0,π)内可导,证明存在ξ∈(0,π),使得f'(ξ)sinξ+2f(ξ)cosξ=0

设f(x)在[0,1]上连续,试证∫(0,π/2)f(|cosx|) 设f(x)在[0.π]上连续,（0,π）内可导 证明存在 设f(x)在上连续,在[0,π]内可导,证明至少存在一点x属于(0,π),使f'(x)=-f(x)cotx 设f(x)在上连续,在[0,π]内可导,证明至少存在一点x属于(0,π),使f'(x)=-f(x)cotx 设f(x)在[0,1]上具有二阶连续导数,且|f''(x)| 设f(x)在[0,1]上连续,且f(x) 高等数学问题：设f(x)在[0,1]上连续,且f(x) 设f(x)在[0,1]上有连续导数,f(0)=0,0 设f(x)在[0,1]上有连续导数,f(0)=0,0 设f(x)在区间[0,1]上连续,且f0)f(1) 设f(x)在[0,1]上连续,且f(t) 设f(x)在[0,π]上连续,(0,π)内可导,证明存在ξ∈(0,π),使得f'(ξ)sinξ+f(ξ)cosξ=0 设f（x）在【0,1】上连续.证明∫（π/2~0)f(cosx)dx=∫（π/2~0)f（sinx）dx 求设f'(x)在[0,a]上连续.f(0)=0,证明|定积分f(x)d(x) 设f(x)在[0,∞)上连续,且当x>0时,0 设f(x)在区间[0,+∞)上连续,且当x>0时,0 设f(x)在[0,π]上连续,且∫f(x)dx=0,∫f(x)cosxdx=0,证明:在[0,π]内有两个不同的p1,p2,使得f(p1)=f(p2)=0. 设f(x)在[0,1]上有连续一阶导数,在（0,1）内二阶可导.