00:01
Okay, so in this question we're looking at the function f of xy is equal to xy over x squared plus y squared.
00:09
And then we're going to be talking about its behavior.
00:13
And so let's look at a computer generated graph.
00:16
It's going to be pretty difficult to visualize this because this is a function that has interesting properties.
00:22
So the behavior in the middle is very hard to describe because the limits as it goes to zero, are undefined.
00:32
So if you have 0, 0, 0.
00:37
And so that makes you very difficult to see what's going on.
00:42
But if you look at the outer limits, so as x and y go to infinity, if x and y both go to negative infinity, or if one goes to infinity and the other goes to negative infinity, and vice versa, you see a very much very different behavior...