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.
本文将一元函数的罗尔定理推广到多元函数中，并给出了一个简洁、颖的证明。
In this paper, the Rolle's theorem of a variadle function is extended to multiple-variable functions. The paper, then, gives a new and simple proof.
中值定理包括罗尔定理、拉格朗日定理和哥西定理。
The middle value theorem consists of Roue. Lagrang and Cauchy theorem.
由此可见罗尔微分中值定理可以是实数的完备性的直接推论。
This implies that Rolles Theorem is the direct consequence of completeness of real numbers.
本文将微积分中的罗尔定理从有限闭区间推广到了半无限区间和无限区间，有助于对罗尔中值定理的理解。
The author generalizes the theorem of Rolle in the calculus from closed interval to semi-infinite interval and infinite interval , which is useful for students to understand theorem of Rolle better.
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.
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.
利用罗尔中值定理给出了函数与其拉格朗日插值函数间的关系，得到中值定理的另外一种形式，并给出了它的应用。
Another form about the median theory and its application is put forward according to the relation between the function and its Lagrange interpolation function in accordance with Rolls median theory.
对广义罗尔定理进行了证明，并应用广义罗尔定理讨论了勒让德多项式的零点。
This paper demonstrates the generalized Rolle theorem and discussed the zero of Legendre polynomials.
罗尔定理在一元微分学处于很重要的地位，本文通过构造函数的思想来探究罗尔定理的应用。
Rolle's theorem plays a very important part in the study of one differential calculus. This paper attempts to explore the application of Rolle's theorem from the perspective of constructing function.
罗尔定理在一元微分学处于很重要的地位，本文通过构造函数的思想来探究罗尔定理的应用。
Rolle's theorem plays a very important part in the study of one differential calculus. This paper attempts to explore the application of Rolle's theorem from the perspective of constructing function.
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