您的位置:首页  > 论文页面

无穷小的阶对于00不定型极限的影响

发表时间:2011-01-15  浏览量:1724  下载量:565
全部作者: 龚谊承,李寿贵
作者单位: 武汉科技大学理学院;武汉科技大学冶金工业过程系统科学湖北省重点实验室
摘 要: 从无穷小的阶的角度探讨影响00不定型极限的原因。通过比较底数和指数作为无穷小的阶的高低,提出并证明2个定理:当底数和指数是同阶无穷小时结果确定为1;当底数是指数的低阶无穷小时结果也确定为1. 另外,通过实例演示定理的应用,说明当底数是指数的高阶无穷小时结果不确定。
关 键 词: 基础数学;极限;无穷小;阶;不确定性
Title: Influence of infinitesimals’ order on limit of exponent function with both base and exponent being infinitesimals
Author: GONG Yicheng, LI Shougui
Organization: College of Science, Wuhan University of Science and Technology; Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology
Abstract: This paper discusses the reasons why the limit is indefinite when the base and exponent are both infinitesimals. By comparing the order of the infinitesimal base and infinitesimal exponent, two theorems are put forward and proved and then illustrated. When the base is of the same order as the exponent, limu(x)v(x) is definitely 1, and so when the base is of the lower order than the exponent. Finally some examples are given to illustrate that limu(x)v(x) is indefinite when the base is of the higher order than the exponent.
Key words: fundamental mathematics; limit; infinitesimal; order; indefiniteness
发表期数: 2011年1月第1期
引用格式: 龚谊承,李寿贵. 无穷小的阶对于00不定型极限的影响[J]. 中国科技论文在线精品论文,2011,4(1):1-3.
 
2 评论数 0
暂无评论
友情链接