关于利用极坐标换元法求二重极限的思考

Some Ideas About Seeking the Solution to Double Limit With the Substitution Technique of Polar Coordinate

在高等数学教学中,二重极限的概念及求法是一个难点。概念难体现在对于定义的理解及二重极限与累次极限的比较,而其求法难具体反映在利用极坐标换元法的使用上,这在大多数大学数学教材上都没有具体提及,本文着重探讨后者,即能不能采用此方法解题,如果能,怎么用,应该注意什么条件。

In higher mathematics teaching,the concept and solution to double limit is a difficult point.Difficult concept embodied in understanding of the definition and comparison of double limit,and its difficult for law reflected in the use of the substitution technique of polar coordinates,which in most university mathematics teaching materials are not specifically mentioned on.This article focuses on the latter,that is,this method can be used problem-solving,if we can,how to,should pay attention to what conditions.