等价无穷小在函数极限计算中的替换技巧  

Replacement technique of equivalent infinitesimal in function limit calculation

作　　者：刘文斐 LIU Wenfei(College of Science,Minzu University of China,Beijing 100081,China)

机构地区：[1]中央民族大学理学院,北京100081

出　　处：《计算机应用文摘》2025年第5期176-178,共3页

摘　　要：针对“高等数学”课程教学中等价无穷小替换的教学难点问题,文章提出在函数极限计算中的替换原则“乘除可替换、加减需慎重”,分类讨论了替换原则的适用范围,基于泰勒公式原理对几种特殊的函数极限等价无穷小替换进行了原因剖析,特别强调了需要慎重等注意事项,在无穷小参与复杂函数极限计算中具有较强的理论指导和支撑。In response to the teaching difficulties of equivalent infinitesimal substitution in the course of“advanced mathematics”,this article proposes the substitution principle of“multiplication and division can be replaced,addition and subtraction need to be cautious”in function limit calculation.The scope of application of the substitution principle is classified and discussed.Based on the Taylor formula principle,the reasons for several special function limit equivalent infinitesimal substitutions are analyzed,with special emphasis on the need for caution and other precautions.It has strong theoretical guidance and support for infinitesimal participation in complex function limit calculation.

关 键 词：等价无穷小 极限计算 等价替换 

分 类 号：O171[理学—数学]