英语释义

1. a theorem in differential calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints there is at least one point where the derivative of the function is equal to the slope of the line joining the endpoints of the curve representing the function on the interval

2. a theorem in integral calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints, there is at least one point in the interval where the product of the value of the function and the length of the interval is equal to the integral of the function over the interval

片语

lagrange s differential mean-value theorem拉格朗日微分中值定理

The Popularity of Mean-Value Theorem中值定理的推广

second mean-value theorem第二中值定理

mean-value theorem of integral积分中值定理

the second integral mean-value theorem第二积分中值定理

cauchy s mean-value theoremcauchy微分中值定理

mean-value theorem for different切比雪夫积分不等式

The Differential Mean-value Theorem微分中值定理

英汉例句

• The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.

  讨论了积分中值定理中间点的单调性、连续性、可导性，给出了一组充分条件，并证明了三个相关定理。

• 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。

• 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。

• 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。

• Study about the first mean value theorem for integrals, which obtain a new results on the mean value asymptotic behavior.

  研究积分第一中值定理，获得了其中值渐近性的一个新结果。

• 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。

• In this paper the monotonicity continuity and derivative of 「intermediate value」 for the first intergral mean value theorem are discussed, and some of their sufficient conditiones are presented.

  讨论了积分中值定理中间点的单调性、连续性、可导性，给出了一组充分条件，并证明了三个相关定理。

• 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。

• 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。

• 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。

• 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。

• 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 presents a generalization of mean value theorem for integrals and discusses the asymptotic properties of mean value of mean value theorem for integral.

  对积分中值定理中间点的渐近性进行研究，给出了推广的积分第一中值定理的中间点的渐近性的一个公式。

• 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。

• 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。

• 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 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。

• This paper intends to discuss and prove the asymptotic behaviour of mean point in second mean value theorem for integrals in concessional terms.

  对积分第二中值定理作了进一步的研究，得到了积分第二中值定理的逆问题及其逆问题的渐进性。

• Two kinds of generalizations of the first mean value theorem of integral for integrable functions with different properties are established in the paper, the results extend the previous conclusions.

  本文建立了两类可积函数的积分第一中值定理的推广形式，推广了已有结论。

• 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。

• 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。