f(x)在[0,1]上连续,在(0,1)内可导,且f(1)=0,求证：存在a(0

f(x)在(0,1)上连续,证明 f(x)在(0.1)上连续且单调增,证明∫[0,1]f(x)dx 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) 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[0,1]上有连续导数,f(0)=0,0 设f(x)在[0,1]上连续,试证∫(0,π/2)f(|cosx|) 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) 证明：函数f(x)=sin(x)/x在(0,1)上是一致连续的 设f(x)在[0,1]上有连续一阶导数,在（0,1）内二阶可导. f(x)=sin1/x在区间（0,1）上是否一致连续?为什么? 设f(x)在[0,1]上有连续导数,且f(x)=f(0)=0.证明 f(x)在(0,1)上连续,f(0)=f(1)=0,证明必存在f''(x)=2f'(x)/(1-x) f(x)在〔0,1〕上连续.f(0)＝f(1)证明存在x使f(x)＝f(x＋0.5) f(x)在[0,pi]上连续,且f(x)sinkx,f(x)coskx在[0,pi]上的积分都是0,1