用极坐标变换求二重极限的定理及推广

A Theorem for Determining Double Limit with Transformation of Polar Coordinates and Its Popularization

运用上、下确界和极坐标变换,化二元函数的重极限的判断和求解为一元函数极限的判断和求解,得到了用极坐标变换求解二重极限的一个定理和一些推论,并推广到用n维球坐标变换求n重极限.

The method of judging and requesting double limit of a binary function is translated in to the method of judging and requesting the limit of one-variable function by supremum and infimum and transformation of n-dimensional spherical coordinates. First,a theorem of requesting double limit with transformation of polar coordinates and some deductions are presented. Finally, a theorem of requesting multiple limits with transformation of n dimensional spherical coordinates is generalized.