函数极限的不存在性研究以及在教学中的应用

The Classlfieation Study on Non-existence of Limit of Functions and its Application in Teaching

本文在考查函数极限定义的基础之上，分析函数极限的不存在性，给出了极限不存在性的精确定义，首次提出对极限不存在进行分类研究，可以分为无穷型，跳跃型，单侧型．发散型和其它型，并且证明该分类的合理性，最后讨论了此种分类在教学实践中的应用。

This paper presents the definition of non-existence of limit of functions as x→x0, and begains to study the classification of non-ekistence of limit of functions. There are five types .i. e. the type of infinity, the type of skip, the type of diyernyet. the one-sided type and the other type. The dissensions of its application to teaching are shown at the end of this paced, There are some examples and some theorems, which are used to explain the suitability of the classification.