Secondly, the Lagrange mean value theorem in some proof of identity and the inequality in a wide range of applications.

其次，拉格朗日中值定理在一些等式和不等式的证明中应用十分广泛。

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This paper gives the new method to prove the cauchy mean value theorem which also may be deduced from the Lagrange mean value theorem.

给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。

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This paper gives the new method to prove the Cauchy Mean Value Theorem, which also may be deduced from the Lagrange Mean Value Theorem.

给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。

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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。

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Finally discusses the Lagrange mean value theorem proof method of constructing auxiliary function in order to expand on the idea of theorem proving.

最后探讨了拉格朗日中值定理证明中辅助函数的构造方法，以此拓展对定理证明的思路。

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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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This paper deals with the forms of higher order of Cauchy′s mean value theorem, from which the author draws an inference of the forms of higher order of Lagrange′s mean value theorem.

本文论述柯西中值定理的高阶形式，并由此推出拉格朗日中值定理的高阶形式。

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This paper deals with the forms of higher order of Cauchy′s mean value theorem, from which the author draws an inference of the forms of higher order of Lagrange′s mean value theorem.

本文论述柯西中值定理的高阶形式，并由此推出拉格朗日中值定理的高阶形式。

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