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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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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