关于二重极限性质和计算的若干问题  

Some problems on properties and calculation of double limit

作　　者：赵莉莉 ZHAO Li-li(School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《佛山科学技术学院学报（自然科学版）》2023年第2期22-29,共8页Journal of Foshan University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561072);云南省教育厅自然科学基金资助项目(2020J0020)。

摘　　要：由于坐标平面上的动点趋于定点的方式有无穷多种,因此,判断二重极限是否存在,以及如何求出二重极限一直都是高等数学中的重点与难点,也是考研数学中的热点。为了让学生更好地掌握二重极限,类比一元函数的极限,证明了二重极限的相关性质,介绍了计算二重极限和判断二重极限是否存在的各种方法,并通过相应的例子加以说明。Because the moving point on the coordinate plane tends to the fixed point in an infinite variety of ways,therefore,to judge whether the double limit exists and how to calculate the double limit is always the key and difficult point in advanced mathematics,but also the hot spot in postgraduate mathematics.In order to make students master the double limit better,this paper proves the related properties of the double limit in detail by analogy with the limit of one variable function,introduces various methods to calculate the double limit and judge whether the double limit exists or not,and illustrates them through corresponding examples.

关 键 词：二重极限 二次极限 极坐标 无穷小量 洛必达法则 

分 类 号：O171[理学—数学]