关于二重极限与累次极限的一些讨论摘要 函数极限既是数学分析中一个重要的概念同时也是一种重要的研究工具，以极限作为工具研究函数是高等数学区别于初等数学的重要特征。二元函数中若自变量从任何方向沿任何路径向定点逼近时，对应的函数值都逼近一确定常数，则称该常数为二元函数在点定点处的二重极限，简称重极限。若两个自变量按一定的先后次序相继逼近定点时，两个一元函数的极限均存在，这就是累次极限。本文主要讨论二元函数的重极限和累次极限在存在性方面的关系以揭示这两种极限之间的内在区别和联系，同时讨论如何借助这种联系简化复杂的重极限的计算。关键词 二重极限 累次极限 存在性 Some discussions on double limit and repeated limitAbstract The limit of function is not only an important concept in mathematical analysis but also an important research tool.In a binary function, if the independent variable approaches the fixed point along any path from any direction, the corresponding function value approaches a certain constant, then the constant is called the double limit of the binary function at the point and fixed point, referred to as the double limit.If two independent variables approach a fixed point in a certain order, the limits of two unary functions exist, which is the recurrent limit.In this paper, we mainly discuss the relation of the existence between the heavy limit and the recurrent limit of the function of two variables, so as to reveal the inner difference and relation between the two kinds of limits, and discuss how to simplify the calculation of the complicated heavy limit with the help of this relation.Key words Double limit Repeated limit Existence 目 录摘 要..............................................................................................................................................1Abstract.............................................................................................................
