关于二重变上限积分的等价无穷小  

On Equivalent Infinitesimals of Variable Upper Limits Double Integrals

作　　者：杨芮 杨铁坪 YANG Rui;YANG Tieping(School of Mathematics Science, Nanjing Normal University, Nanjing 210023, PRC;School of Mathematics and Information, China West Normal University, Nanchong 637009, PRC)

机构地区：[1]南京师范大学数学科学学院,江苏南京210023 [2]西华师范大学数学与信息学院,四川南充637009

出　　处：《高等数学研究》2020年第2期73-76,共4页Studies in College Mathematics

摘　　要：将二重变上限积分看作是一类特殊的一元诱导函数,本文给出了两种二重变上限积分的定义方式,分别对积分限和被积函数做相应的等价无穷小量替换.在一定的条件下,替换后的二重变上限积分与替换前的二重变上限积分是等价无穷小,从而得到一类求极限的方法,并给出了应用实例.Two kinds of one-variable functions expressed by variable upper bounds double integrals are studied in this paper.We prove that by replacing the integral bounds and functions respectively with the equivalent infinitesimals in each kind will result the equivalent infinitesimals under certain conditions.Applications are illustrated.

关 键 词：二重变上限积分 一元诱导函数 等价无穷小 

分 类 号：O171[理学—数学]