无穷小量

本文主要探索利用Taylor公式对无穷小量的阶进行估计，从而有效地判断出二元函数极限的存在性。

In this paper , Taylor 's formula is used to estimate the order of infinitesimal , so that the limit existence about some binary function is estimated effectively .

等价无穷小量代换的推广和应用

The Extension and Application of the Equivalent Infinitesimal Replacement

有时候把无穷小量dx和dy描述成正在消失的或者刚出现的量。

The infinitely small " dx " and " dy " were sometimes described as vanishing or incipient quantities .

牛顿说他已放弃了微元或无穷小量。

Newton says he has abandoned the infinitesimal or infinitely small quantity .

无穷小量部分代换求极限成立的充要条件

The Sufficient and Necessary Condition when Requesting Limit by Infinitesimal Portion Commutation

非标准分析中无穷小量阶的研究

A study of infinitesimal quantity order in off-standard analysis

关于多元高阶无穷小量的一个注记

A Note about the Higher Order Infinitesimal of Multivariate

关于无穷小量乘积的讨论

On the Infinite Product of the Infinitely Small Quantity

无穷小量在求函数极限中的应用

The Application of Infinitesimal Quantity in Getting Function Limit

关于用等价无穷小量代换定理求极限的一个推广命题

A Promoted Proposition on Asking the Limit with Equivalence Infinite Small Quantity Substitution Theorem

利用无穷小量的代换性质推导了3种计算方法，并举例说明了应用这些方法求函数的极限。

Examples are showed as to how to apply these methods to calculate limit .

应用等价无穷小量的代换方法求极限

Limit Calculation by the Equivalent Infinitesimal Replace Methods

无穷小量的等价代换在代数和的极限运算中的应用

The Application on Substitution of Equivalent Infinite Small in Algebra Sum 's Limiting Operation

无穷小量的等价定理及其应用

An infinitesimal equivalence theorem and its application

随机无穷小量及其商分布

Random infinitesimal and its quotient distributions

一个与无穷小量有关的命题

A Proposition on the Infinitesimal Number

用等价无穷小量替换求极限是一种常用、方便、有效的方法。

Getting limit with substitution of equivalence infinitesimal is a common , convenient and efficient way .

无穷小量的思考

Thinking About the Infinitesimal

对用等价无穷小量代换定理求极限进行了推广。

This paper promotes the proposition on asking the limit with equivalence infinite small quantity instead of theorem .

在19世纪末的数学公理化运动中，极限取代了无穷小量成为微积分的基础。

The limit became the basis of differential in place of infinitesimal in the movement of 19th mathematical axiom .

采用非标准分析观点，定量地讨论了无穷小量的阶并给出阶的应用。

Using the view of the off-standard analysis , this paper discusses the order of infinitesimal quantity and gives out the application of the order .

本文得到了等价无穷小量代换的一些结论，并着重讨论了等价无穷小量的代换在代数和的极限运算中的应用。

This article presents some conclusion of substitution about equivalent infinite small , and stress on discussing the application in calculation of limit about algebra sum .

讨论了无穷小量的代数和的等价代换定理，以及1∞型和00型未定式极限的等价无穷小量代换定理及其应用。

This paper studied the equivalent replacement of infinitesimal algebraic sum , and also gives the theory and application of the equivalent infinitesimal replacement about indefinite forms such as 1 ∞, 00 ect .

本文通过对一道题的分析、求解，进一步剖析了无穷小量理论，并对数零是唯一可作为无穷小的常量进行了说明。文中给出计算示例。

With the analysis of a example , the article gives a further explanation of the theory of infinitesimal and explains that the number " zero " is the only constant as an infinitesimal .

文章通过对无穷小量与无穷大量的阶的概念研究，用阶的估计讨论数学分析中数列、函数及级数收敛问题，也为收敛问题深入研究提供了一种方法。

This paper studies the concept of infinitesimal and infinity , and discusses the convergence of sequence , function and series with the estimation of the orders . A kind of method for studying convergence is offered .

讨论了高等数学中无穷大量与无穷小量的关系，无穷大量的性质，无穷大量的等价。

This paper studies the relationship between infinitely large quantity and infinitely small quantity , the nature of infinitely large quantity and the equivalence of infinitely large quantity .