关于二重极限教学的一点注记——与《微积分解题方法与技巧》一书的作者商榷

On the Teaching of Double Limit

本文首先对《微积分解题方法与技巧》一书中某题的解法提出质疑;然后研究了三种不同情形下可以得出不同的结果;进而否定了该书的解法;最后指出,被高等数学广泛采用的“极坐标代换法”不能直接用于二重极限,并给出了理论上的解释和证明。

This paper begins with the query of the resolution to one of the problems in the book'the resolutions and skills of differential and integral calculation't hen introduces three different conditions under which we can come to three different conclusions, hereby denies the resolution of the book. This paper ends with the viewpoint-the method of the polar coordinate transformation that is extensively used in advanced mathematics cannot be directly used in double limit, and the theoretical explanation and proof are given as well.