作业帮设f(x)在[a,b]上连续,在(a,b)内可导,(0
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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
证：
记g(x)=lnx,显然g(x),f(x)在[a,b]上满足柯西中值定理条件
则存在一点ξ∈(a,b)使得
[f(b)-f(a)]/[g(b)-g(a)]=f'(ξ)/g'(ξ)
即[f(b)-f(a)]/[lnb-lna]=f'(ξ)/(1/ξ)
有f(b)-f(a)=ln[b/a]ξf′(ξ)
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