设f(x)在[0,π/2]上连续,在(0,π/2)内可导,且f(π/2)=0,试证存在一点ζ∈（0,π/2)使f（ζ）+tanζ*f ‘（ζ）=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[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[0,1]上连续,证明在该区间上f^2(x)的积分>=(f(x))的积分的平方 设f(x)在[0,1]上有连续一阶导数,在（0,1）内二阶可导. 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 证明:设f(x)在[a,b]上连续,在(a,b)内可导,(0 设f(x)在[a,b]上连续,在(a,b)上可导(0 设函数f(x)在[a,b]上连续,在(a,b)内可导(0 设f(x)在[a,b]上连续,在(a,b)内可导,(0 设f(x)在[a,b]上连续,在(a,b)内可导(0