主题：【求教数学问题】如何判别这个函数在原点附近的性质？ -- 晨枫

school level math, but you must noticed that at (0,0) it is a special point for the first derivative. At this point, the value is different when you approach from different quadrates. When you approach from 1st quadrate, x>0 and y> 0 so the limit is 1. From second quadrate, x>0 and y< 0 so it is –1. and so on.

To calculate the above, simply use the 'delta' approach so only the lowest powered items (2x and 2y) are count.

This is obviously a saddle like surface. Not exactly sure what else they what to know.