1)  infinitesimal [英][,ɪnfɪnɪ'tesɪml]  [美]['ɪnfɪnə'tɛsəmḷ]

1.
The Extension and Application of the Equivalent Infinitesimal Replacement;

2.
An infinitesimal equivalence theorem is established in this paper.

3.
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.

2)  infinitesimal quantity

1.
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.

2.
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.

3)  infinitely small quantity

1.
Theorem 1 and 2 about ratio of two infinitely small quantity function monotonous are obtained.

2.
In this paper,we disscus the poerations of infinitely small quantity and get some result.

3.
In this note, we construct some examples to show that the infinitely product of the infinitely small quantity may be not infinitely small quantity.

4)  infinite small quantity serie

5)  infinitesimal increment

6)  higher order indefinite small

 无穷小量infinitesimal    以数零为极限的变量。确切地说，当自变量x无限接近x0(或x的绝对值无限增大)时，函数值f(x)与零无限接近，即f(x)＝0(或f(x)＝0)，则称f(x)为当x→x0(或x→∞)时的无穷小量。例如，f(x)＝(x－1)2是当x→1时的无穷小量，f(n)＝是当n→∞时的无穷小量，f(x)＝sinx是当x→0时的无穷小量。特别要指出的是，切不可把很小的数与无穷小量混为一谈。