设y=f(x)在[0,1]连续,在(0,1)可导,且f(0)=1,f(1)=0.
设f(x)在[0,1]上有二阶连续导数,且满足f(1)=f(0)及|f''(x)|
设f(x)在[0,1]上有连续导数,且f(x)=f(0)=0.证明
设函数f(x)在(-∞,+∞)可导,且满足f(0)=1,f'(x)=f(x),证明f(x)=e^x
证明:设f(x)在(-∞,+∞)连续,则函数F(x)=∫(0,1)f(x+t)dt可导,并求F'(x)
设f(x)在[a,b]上连续,在(a,b)可导且f'(x)小于等于0,F(x)=(1/x-a)∫[0-->x]f(t)d
设函数f(x)在x=1连续,且f(x)/(x-1)的极限存在,求证f(x)在x=1可导.
设f(x)在[0,1]上连续,在(0,1)可导,且f(0)=f(1)-0,f(1/2)=1/2.证明:在(0,1)内至少
一道高数题,设函数f(x)在[0,+∞)上连续,且f(x)=x(e^-x)+(e^x)∫(0,1) f(x)dx,则f(
设f在0到1上连续且可导,3*定积分上1/3下0e^(1-x^2)f(x)dx=f(1),证明存在t在(0,1)使f'(
设f(x)为可导函数,且满足条件lim(x->0)[f(1)-f(1-x)]/2x=1,则曲线y=f(x)在(1,f(x
设f(x)在[0,1]上连续且可导,又f(0)=0,0≤f'(x)≤1 试证:[ ∫^(0,1)f(x)dx]^2≥∫^
设函数f(x)在(-∞,+∞)上连续,且f(x)=e^x+1/e∫(0,1)f(x)dx,求f(x)