函数形式的单调有界原理及其证明  

Monotone Bounded Principle of Function Form and its Proof

作　　者：徐芹 XU Qin(Department of Science,Dingxi Campus of Gansu University of Chinese Medicine,Dingxi 743000,China)

机构地区：[1]甘肃中医药大学定西校区理科教学部,甘肃定西743000

出　　处：《中央民族大学学报（自然科学版）》2020年第4期31-34,共4页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：甘肃省2019年度高等学校创新能力提升项目(2019A-195);甘肃中医药大学定西校区创新企业教改项目(2020XJJG29)。

摘　　要：极限的存在性是研究函数极限的前提和基础。函数的单调有界原理是判断函数极限存在的重要方法之一,但在应用过程中极易与数列的单调有界原理相互混淆。为此,本文通过比较数列和函数单调有界原理的异同,详细叙述和证明了不同类型函数极限的单调有界原理,易于学生理解和掌握。The existence of limit is the premise and foundation of studying function limit.The monotone bounded principle of function is one of the important methods to judge the existence of function limit,but it is easily confused with the monotone bounded principle of sequence in the application process.Therefore,by comparing the difference between the monotone bounded principle of sequence of numbers and the monotone bounded principle of function,the monotone bounded principle of different types of function limit is described and proved in detail,which is easy for students to understand and master.

关 键 词：单调有界 函数 极限 确界 

分 类 号：O17[理学—数学]