摘要
为了要更精确地比较无穷小的形态,需要用数字来表示它们的阶.结合无穷小的阶数的定义,给出无穷小阶数的相关性质,并统一从无穷小的阶数的观点来回答无穷小内容学习的几个难点,什么条件下两个无穷小才可以进行比较?在用等价无穷小代换求极限中,什么条件下相减和相加的因子能看成一个整体直接代换?最后给出无穷小定阶的常用方法.
Numbers are needed to illustrate the order of infinitesimal for comparing their orders more precisely.The paper states the feature of the infinitesimal order under the guidance of its definition and deal with several difficulties of it:When is the time to compare them?When is the time to treat the form of addition and subtraction as a whole in the equivalent infinitesimal replacement to seek the limit?At last,the usual methods for the order are listed.
作者
杨吉英
张娟
蔡姗姗
YANG Ji-ying;ZHANG juan;CAI Shan-shan(Department of Mathematics,Baoshan University, Baoshan Yunnan 678000,China;Department of Engineering,Oxbridge College,Kunming University of Science and Technology,Kunming 650106,China;Department of Mathematics and Statistics,Puer University,Puer Yunnan 665000, China)
出处
《大学数学》
2021年第5期104-108,共5页
College Mathematics
基金
云南省应用基础研究项目(2017FD140)
云南省教育厅科学研究基金项目(2018JS752)。
关键词
无穷小
无穷小的比较
无穷小的阶数
infinitesimal
comparison of infinitesimal
infinitesimal order
