本文用待定系数法证明拉格朗日定理与柯西定理。
In this paper, we present the proofs of Lagrange Theory and Cauchy Theory. By this method we may determine coefficient.
本文就罗尔定理、拉格朗日定理和柯西定理三者的区别与联系作了分析与探讨。
The paper makes an analysis and inquiry about the differences among the Roue Theorem. Lagrange Thoorem and Cauchy Theorem.
讨论具有某种特征映射的类似柯西积分定理的结论。
A discussion on some characterized mapping conclusions similar to Cauchy integral 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.
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.
本文介绍了柯西中值定理的多种证明方法及其应用。
This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
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.
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.
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.
特别是那些没有听过的柯西准则的同学：见定理12 ！
In particular, those of you that never heard of Cauchy's criterion: see Theorem 12!
柯西不等式、刘维尔定理。
但是阅读定理的陈述——大部分将会在课堂上讲解，特别是那些没有听过的柯西准则的同学：见定理12 ！
BUT, read the theorem statements — which will be covered in the lectures, mostly. In particular, those of you that never heard of Cauchy's criterion: see theorem 12!
但是阅读定理的陈述——大部分将会在课堂上讲解，特别是那些没有听过的柯西准则的同学：见定理12 ！
BUT, read the theorem statements — which will be covered in the lectures, mostly. In particular, those of you that never heard of Cauchy's criterion: see theorem 12!
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