作业帮设f(x)在[a,b]上连续,在(a,b)内f(x)可导且f(x)≠0,f(b)=f(a)=0.试证对任意的实数α,存在ξ∈(a,b),使f'(ξ)+αf(ξ)=0
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![设f(x)在[a,b]上连续,在(a,b)内f(x)可导且f(x)≠0,f(b)=f(a)=0.试证对任意的实数α,存在ξ∈(a,b),使f'(ξ)+αf(ξ)=0](/uploads/image/z/14330448-0-8.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%28a%2Cb%29%E5%86%85f%28x%29%E5%8F%AF%E5%AF%BC%E4%B8%94f%28x%29%E2%89%A00%2Cf%28b%29%3Df%28a%29%3D0.%E8%AF%95%E8%AF%81%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84%E5%AE%9E%E6%95%B0%CE%B1%2C%E5%AD%98%E5%9C%A8%CE%BE%E2%88%88%28a%2Cb%29%2C%E4%BD%BFf%27%28%CE%BE%29%2B%CE%B1f%28%CE%BE%29%3D0)
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设f(x)在[a,b]上连续,在(a,b)内f(x)可导且f(x)≠0,f(b)=f(a)=0.试证对任意的实数α,存在ξ∈(a,b),使f'(ξ)+αf(ξ)=0
设f(x)在[a,b]上连续,在(a,b)内f(x)可导且f(x)≠0,f(b)=f(a)=0.试证对任意的实数α,存在ξ∈(a,b),使f'(ξ)+αf(ξ)=0
设f(x)在[a,b]上连续,在(a,b)内f(x)可导且f(x)≠0,f(b)=f(a)=0.试证对任意的实数α,存在ξ∈(a,b),使f'(ξ)+αf(ξ)=0
令F(x)=e^(kx)f(x),在[a,b]上用罗尔定理可以证出f'(§)+kf(§)=0.
原题就是这样的?
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