无穷小的性质研究

The Properties of Infinitesimal

本文研究了极限的四则运算,提出了无穷小和无穷大的四则运算和未定式极限的关系,并举例说明泰勒公式结合等价无穷小计算极限的思路,同时给出了无穷小阶的定义及其关系,还证明了一个高阶无穷小、一个等价无穷小的定理。

In this paper, we study the four operations of the limit, and propose the relationship between the infinitesimal and infinite quadruple operations and the infinitive limit, and illustrate the idea of Taylor＇s formula combined with the equivalent infinitesimal calculation limit, and give the definition of infinitesimal order and its relationship. Prove a high-order infinitesi-mal, an equivalent infinitesimal theorem.