无穷小比较的意义及其应用  

The Significance and Application of Infinitesimal Comparison

作　　者：周正岳 黄丽芹 ZHOU Zhengyue;HUANG Liqin(Foundation Department,Army Engineering University of PLA,Nanjing 210000,China)

机构地区：[1]陆军工程大学基础部,江苏南京210000

出　　处：《高等数学研究》2022年第4期19-21,共3页Studies in College Mathematics

摘　　要：对《高等数学》教材中无穷小比较的解释进行了解读,并通过研究无穷小之比的极限与函数的导数之比的联系,分析了无穷小比较的意义,以及无穷小比较在计算极限中的应用,给出了一种洛必达法则的证明方法.This paper interprets the explanation of infinitesimal comparison in the textbook of Advanced Mathematics, and analyzes the significance of infinitesimal comparison by studying the relation between the limit of the ratio of infinitesimals and the ratio of derivative functions, and the application of infinitesimal comparison in calculating the limit, and gives a proof of L’Hopital’s rule.

关 键 词：无穷小比较 洛必达法则 同阶无穷小 高阶无穷小 

分 类 号：O13[理学—数学]