设f(x)在[0,a]上连续,在(0,a)内可导,且f(0)=0,f(x)的导数单调增,证当0

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设f(x)在[0,a]上连续,在(0,a)内可导,且f(0)=0,f(x)的导数单调增,证当0
设f(x)在[0,a]上连续,在(0,a)内可导,且f(0)=0,f(x)的导数单调增,证当0

设f(x)在[0,a]上连续,在(0,a)内可导,且f(0)=0,f(x)的导数单调增,证当0
令g(x)=f(x)/x,x∈[0,a] g'(x)=[xf'(x)-f(x)]/x^2 另H(x)=xf'(x)-f(x) H'(x)=f'(x)+xf''(x)-f'(x)=xf''(x) ∵f(x)的导数单调递增 ∴f''(x)≥0 显然x>0 所以H'(x)≥0 ∴H(x)为在(0,a)单调递增 ∴H(x)≥H(0)=0-f(0)=0 ∴g'(x)≥0 ∴g(x)在(0,a)上单调递增 ∴当0

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 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,且a 设函数f(x)在[a,b]上连续,a 设f(x)在[a,b]上连续,且a 设f(x)在[a,b]上连续,且a 设f(x)在[a,b]上连续,a 设函数f(x)在[a,b]上连续,a 设函数f(x)在对称区间【-a,a】上连续,证明∫(-a,a)f(x)dx=∫(0,a)[f(x)+f(-x)]dx 【50分高数微积分题】设f(x)在[a,b]上连续,在（a,b）内可导 f(a)f(b)>0 f(a)f[(a+b)/2] 设f(x)在[a,b]上连续,在(a,b)内可导,f(a)f(b)>0,f(a)f[(a+b)/2] 设函数f(x)在[a,b]上连续,在(a,b)可导,且f(a)*f(b)>0,f(a)*f((a+b)/2) 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)=(f(x)-f(a))/(x-a),(x>a)其中f(x)在[a,+∞）上连续,f''(x)在（a,+∞)内存在且大于0,求证F（x)在（a,+∞)内单调递增.