一道全国大学生数学竞赛试题的解法辨析  

The Right and Wrong Discrimination of a Question in the Mathematics Competition for College Students

作　　者：滕吉红[1] 鲁志波[1] 张启慧[1] 王乾亮 TENG Jihong;LU Zhibo;ZHANG Qihui;WANG Qianliang(Department of Basic Course,Information Engineering University,Zhengzhou 450000,China)

机构地区：[1]信息工程大学基础部,河南郑州450000

出　　处：《高等数学研究》2023年第5期4-6,66,共4页Studies in College Mathematics

基　　金：信息工程大学教育教学研究重点课题(JXYJ2022A002)。

摘　　要：从第11届全国大学生数学竞赛中一道求极限的题目入手,对学生给出的几种方法进行了辨析,指出了解法中的错误所在,分析了错误产生的原因,揭示了学生在等价无穷小的概念、等价无穷小代换方法和极限四则运算法则等知识的理解与应用方面的误区,最后从题目训练的意义、题目设计原则和题目训练方法的角度阐述了如何通过题目训练强化对数学概念、数学理论、数学方法的巩固和数学思维的培养.Several approaches to a question in the 11 th Chinese Mathematics Competition for College Students are presented,followed by the right and wrong discrimination,which reveal the misunderstanding of the replaceable principles of equivalent infinitesimal and the arithmetic operations of limits.The significance of problem solving,the design rules,and the training of problem solving are proposed to consolidate mathematical concepts,theory,and methods,and to cultivate mathematical thinking.

关 键 词：等价无穷小 未定式 数学思维 

分 类 号：G642.2[文化科学—高等教育学]