A Note on The Theorem of Equivalent infinitesimal Replacement;
等价无穷小替换定理的一点注记
On the product of infinite infinitesimals;
关于无穷多个无穷小之积
On equivalent transformations of infinitesimals and their popularization;
关于无穷小的等价替换及其推广
Theorem 1 and 2 about ratio of two infinitely small quantity function monotonous are obtained.
对文献[1]给出的一个函数单调性的判别命题进行推广,得出两个无穷小量之比的单调性的判别命题1,2。
In this paper,we disscus the poerations of infinitely small quantity and get some result.
讨论了无穷个无穷小量作和、积运算后是否仍为无穷小量,得到的结论论是:无限个无穷小量的和、积未必收敛,即使收敛,也未必是无穷小量。
In this note, we construct some examples to show that the infinitely product of the infinitely small quantity may be not infinitely small quantity.
本文由有限个无穷小量的乘积仍是无穷小量的证明入手 ,给出无穷多个无穷小量的乘积不一定是无穷小量的例子 ,并根据这种方法得到无穷多个无穷大量的和也不一定是无穷大量的结
The Extension and Application of the Equivalent Infinitesimal Replacement;
等价无穷小量代换的推广和应用
An infinitesimal equivalence theorem is established in this paper.
建立了一个无穷小量等价的定理，文献１中的结果可作为本文定理的一个简单应用。
This paper takes the infinitesimal as an entrance to derivative and shows the essential of derivative concept step by step and therefore enhances the students to comprehend this concept.
导数是高等数学中的一个重要概念,讨论了一种不同于目前多数教材中介绍导数概念的方法,以无穷小量为切入点,一步步过渡到导数的概念等,揭示了导数概念的本质,强化了学生对这一概念的理解。
In this paper,the link between infinitesimal quantity and some important notions in differential and integral calculus,and the simple application of infinitesimal in limit operation are discussed.
讨论了无穷小量与微积分中几个重要概念的联系和无穷小在极限运算中的简单应用。
In teaching mathematics, we should use geometric figures more in explaining concepts, attach importance to ratio limit and infinitesimal quantity, employ the regular methods, pay attention to the specific skills and help them analyze and solve problems.
在教学中应多用几何图形介绍概念;突出比值极限,重视无穷小量;立足常规方法;注意特殊技巧;引导学生分析、解决问题。
infinitesimal area
无穷小邻域[面积]
Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.
推论1常数与无穷小的乘积是无穷小。
Corollary 1 The product of a constant and an infinitesimal is an infinitesimal.
推论2有限个无穷小的乘积是无穷小。
Theorem 1 The sum of finite number of infinitesimal is an infinitesimal.
定理1有限个无穷小的和也是无穷小。
Notes On Infinity And Infintesimal;
关于无穷小与无穷大关系的一点注记
Some Sufficient Conditions about the Product of Countable Infinitesimal for Infinitesimal;
可列个无穷小乘积仍为无穷小的若干充分条件
The Thinking about the Product of Infinite Infinitesimals;
关于无穷多个无穷小的乘积的一些思考
Capable of having values approaching zero as a limit.
近零的，极小的无穷小地接近于零的
Infinitesimal Quantum gl_n and Associated Little q-Schur Algebras;
无穷小量子gl_n和相关的小q-Schur代数
An immeasurably or incalculably minute amount or quantity.
无穷小的数量非常小，几乎无法测量的数量
And roam it does, from the infinitesimal to the infinite, from the subatomic realm to the far reaches of the universe.
并且智慧遨游，从无穷小到无穷大，从亚原子王国到遥远的宇宙。
Newton says he has abandoned the infinitesimal or infinitely small quantity.
牛顿说他已放弃了微元或无穷小量。
Seeking Functional Limit by Equivalent Infinitesimal Replacement;
利用“等价无穷小的替换”求函数的极限
The Simple Way of Calculating Limit by Using Equivalence Infinit Small;
利用等价无穷小求解极限的简便方法
A Research of Equivalent Infinitesimal Substitution Method Applied to Limit Operation;
用"等价无穷小替代法"求极限的研究
Limit Calculation by the Equivalent Infinitesimal Replace Methods;
应用等价无穷小量的代换方法求极限
The application of infinitesimal institution in [1~∞]form limit
无穷小替换在求[1~∞]型极限中的应用
This paper gives the equivalent keplacement of infinitesimal algebraic sum, and also gives the theory and application of the equivalent infinitesimal replacement about indefinite forms such as1?∝,0?° ect.
给出无穷小代数和的等价代换，以及“1∞型“00”型未定式等价无穷小代换定理及应用。