[Everyday Mathematics]20150108
2015-01-05 20:38
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设 $f$ 在 $(a,b)$ 上 $n+1$ 次可导, 且 $$\bex \ln\frac{f(b)+f'(b)+\cdots+f^{(n)}(b)}{f(a)+f'(a)+\cdots+f^{(n)}(a)}=b-a. \eex$$ 试证: 存在 $c\in (a,b)$, 使得 $$\bex f^{(n+1)}(c)=f(c). \eex$$
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