微分中值定理是微分学的基本定理。
Differential medial value theorem is the basic theorem of the calculus.
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.
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.
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.
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.
主要讨论了第二积分中值定理“中值点”的渐近性和渐近速度。
This paper discusses the asymptotic rate of "mean value point" in second mean value theorem for integrals.
针对对称导数、对称偏导数，给出了一些新形式的微分中值定理。
In this paper, symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
本文利用积分上限函数给出证明中值定理及类似问题的一种方法。
This paper applies an integral upper limit functions to giving a method for the solution of the problems similar to those as the proven mean value theorem.
利用泰勒公式，给出中值定理“中值点”渐近性质的一个定量刻画。
Using the Taylor formula, gives the theorem of mean "the value point" an approach nature quota portray.
本文将实分析中的微分中值定理推广到复分析中，得到了相应的结果。
In this paper, the differential mean value theorem of real analysis is extended to the complex analysis and correspondence results are obtained.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
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.
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。
Finally, the condition and result of integral mean-value theorem are also improved combined with the Lagrange mean value theorem of differentials.
对曲面积分中值定理，给出了一个新的证明，并举出相关例子加以应用。
In this paper, a new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
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.
讨论了二元函数中值定理中间值的渐近性质，给出了一个相关反问题的解。
The asymptotic properties of mean value in the mean value of bivariate functions are discussed, a solution is presented for related inverse problem.
构造辅助函数是利用微分中值定理解决问题的关键，构造辅助函数的方法较多。
Constructing auxiliary functions is the key in using differential mean value theorem to solve problems; there are many methods for constructing auxiliary functions.
给出了微分中值定理的一个推广形式，并将所得结果应用于凸函数性质的研究。
This article gives a spreading form of the mean value theorem of differential and applies the gained results to the quality of convex function.
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.
文章根据最小曲率半径定义和中值定理，通过极值分析方法来确定桩基极限荷载。
Based on the minimum curvature radius definition and mid value theorem, the pape gives the method of determining the limit load of pile foundation through extreme value analysis.
以分割区域d为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式。
Basing on a partition of region d, we generalize the differential mean-value theorems for analytic functions and conjugate analytic functions to a high order case.
介绍一种通过槽区实测资料的相关分析，利用中值定理计算灌溉人渗系数的方法。
This paper introduced a method to calculate irrigation permeated coefficient in utilizing media value theorem.
应用闭区间连续函数性质和实数连续性定理，给出证明广义中值定理的一个新思路。
Closed interval continuous function and continuity theorem of real number apply to a novel demonstration of general theorem of the mean.
考虑了环境辐射影响，基于中值定理推导并定义等效波长，用于简化测温数学模型。
The equivalent wavelength is deduced and defined by considing the influence of ambient radiation, and adopted to simplify the mathematical model of temperature measurement.
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.
讨论了第一类曲线积分中值定理“中间点”的渐近性质，得到了更具一般性的新结果。
This paper is devoted to studying the asymptotic behavior of the intermediate point in the mean value theorem for first form curve integrals. A general result is obtained.
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.
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.
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