应用区间套定理给出了拉格朗日中值定理一个新的证明。
A new way to prove Lagrange's mean value theorem is given using the theorem of interval nest.
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。
Secondly, the Lagrange mean value theorem in some proof of identity and the inequality in a wide range of applications.
总结了高等数学中拉格朗日中值定理五个方面的应用，并举例加以说明。
The paper sums up the application of Lagrange mean theorem in five aspects in high mathematics, and give an example to illustrate its application.
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。
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.
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。
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。
This paper gives the new method to prove the Cauchy Mean Value Theorem, which also may be deduced from the Lagrange Mean Value Theorem.
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。
Finally discusses the Lagrange mean value theorem proof method of constructing auxiliary function in order to expand on the idea of theorem proving.
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。
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.
其证明方法关键在于构造一个辅助函数，再应用罗尔中值定理推出拉格朗日中值定理的结论。
Its key proof is to construct an auxiliary function, which is used by Roll's theorem to reach a conclusion of Lagrange's theorem.
本文根据区间套的方法，证明柯西中值定理，而把罗尔定理和拉格朗日中值定理作为它的推论。
Cauchy's theorem of the mean is proved by means of nested intervals, with Rolle's and Lagrange's theorems of the mean as its corollaries.
本文根据区间套的方法，证明柯西中值定理，而把罗尔定理和拉格朗日中值定理作为它的推论。
Cauchy's theorem of the mean is proved by means of nested intervals, with Rolle's and Lagrange's theorems of the mean as its corollaries.
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