极限两类问题中海涅定理的应用  

The Application of The Heine Theorem in Two Kinds of Limit Problems

作　　者：张慧芬 张珍 ZHANG Huifen;ZHANG Zhen(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报(自然科学版)》2025年第1期36-38,共3页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西大同大学教学改革创新项目[XJG2023253]。

摘　　要：海涅定理是山东大学版高等数学课本中函数极限性质中的一部分内容,书上内容篇幅有限,定理内容描述又抽象,使得学生理解起来有点困难。从海涅定理的应用着手,阐述了用其解决极限问题中两类题型的可行性。通过分类举例思想,使得学生对这一知识点掌握得更具体化、实用化,完成学科构建的目标,能够轻松独立完成课后作业题。Heine theorem is a part of function limit property in Shandong University higher mathematics textbook.Because of the limited space and abstract description of the theorem,it is difficult for students to understand it.Starting from the applications of Heine theorem,this paper expounds the feasibility of using it to solve two kinds of limit problems.Through the idea of classification and example,the students can master the knowledge more concretely and practically,and achieve the goal of discipline construction,and can easily complete the homework after class independently.

关 键 词：函数极限 数列极限 海涅定理 

分 类 号：O173[理学—数学]