In this paper, a new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
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。
This article gives a spreading form of the mean value theorem of differential and applies the gained results to the quality of convex function.
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。
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.
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。
In this paper, we introduce a new concept of generalized derivative, and derive its operational rules and the mean value theorem of continuous functions.
文章提出了一种广义导数的概念，得到了广义导数的运算法则，以及连续函数的中值定理。
In this paper, the author USES the contour integral in analytic function to functional analysis, and obtains the mean value theorem of operator-valued functions.
本文把复变函数的围道积分应用于泛函分析，对一般的线性闭算子得到了算子值函数的中值定理。
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.
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 points out and revises some errors in the results found in four articles concerning the asymptotic behavior of the "Intermediate points" of the mean value theorem.
本文指出了有关微分中值定理“中间点”的渐近性四篇文章的结果中的错误，并给予修正。
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。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
讨论泰勒中值定理中中值点的连续性及可导性问题，给出泰勒中值定理中中值点连续及可导的充分条件，同时给出计算其导数的公式。
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 article explores the four ways for solving integral inequality with the nature of definite integral, mean value theorem of differentials, Schwarz inequality and double integral.
本文利用定积分的性质、微分中值定理、施瓦兹不等式、二重积分等内容，研究了积分不等式的四种证法。
Results the value distribution properties of this function were solved and an interesting mean value theorem was obtained.
结果关于这个函数的值分布性质，给出了一个有趣的均值定理。
This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.
本文介绍了柯西中值定理的多种证明方法及其应用。
A new way to prove Lagrange's mean value theorem is given using the theorem of interval nest.
应用区间套定理给出了拉格朗日中值定理一个新的证明。
In this article, the author has proved the theorem of "middle point" in the second integral mean value.
给出并证明了关于积分第二中值定理“中间点”的渐近性定理。
By increasing the condition of the integral mean value theorem, we prove that the existence of intermediate point and the existence of interval are corresponding to each other.
给出了积分中值定理的一个注记，证明了中值点的存在性与覆盖中值点的区间的存在性是相互对应的。
Constructing auxiliary functions is the key in using differential mean value theorem to solve problems; there are many methods for constructing auxiliary functions.
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。
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。
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。
In this paper, second mean value theorem for integrals is studied, and some results of the inverse problem of the theorem are obtained.
给出了在各种情况下积分第二中值定理“中间点”的渐近性的几个结论，相信在积分学中有着很重要的作用。
This paper discusses the asymptotic rate of "mean value point" in second mean value theorem for integrals.
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。
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。
Using the Taylor formula, gives the theorem of mean "the value point" an approach nature quota portray.
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。
According to the theorem of integral mean value it is proved in this paper that by means of probability integral the subsidence equivalent curve is a circle or a ellipse.
文中还根据积分中值定理证明了应用概率积分法求得的下沉等值线是椭圆形或圆形。
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.
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。
In this paper, the differential mean value theorem of real analysis is extended to the complex analysis and correspondence results are obtained.
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。
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.
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。
Based on the integral inequality and other quality proved, the paper discusses the conclusion of the mid-value in theorem of integration mean which is got in open interval.
在证明了定积分不等式等性质的基础上，给出并证明了积分中值定理的中值在开区间内取得的结论。
Based on the integral inequality and other quality proved, the paper discusses the conclusion of the mid-value in theorem of integration mean which is got in open interval.
在证明了定积分不等式等性质的基础上，给出并证明了积分中值定理的中值在开区间内取得的结论。
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