mean value theorem [数] 中值定理 ; [数] 均值定理 ; 平均值定律 ; [数] 平均值定理
differential mean value theorem 微分中值定理
integral mean value theorem 积数指数
Gauss Mean value theorem 高斯平均值定理
extended mean value theorem 广义均值定理
Lagrange mean value theorem 拉格朗日中值定理 ; lagrange中值定理
Cauchy mean value theorem 柯西中值定理 ; cauchy中值定理 ; 柯西均值定理
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This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.
本文介绍了柯西中值定理的多种证明方法及其应用。
Finally, the condition and result of integral mean-value theorem are also improved combined with the Lagrange mean value theorem of differentials.
最后，结合拉格朗日微分中值定理改进了积分中值定理的条件和结论。
On the basis of these theories, Rolle mean value theorem, Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.
在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理。
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