calculating limes aprouching infinity for two variables function

Lampa

New member
Joined
Mar 18, 2018
Messages
3
Hi.
I have been wondering how to show that two variables function is greater than zero. I thought about calculating minima and from Intermediate value theorem showing that it isn't negative. So how can I calculate
lim(x,y)-> (∞, ∞) f(x,y) , lim(x,y)-> (∞,-∞) f(x,y), lim(x,y)-> (-∞,-∞) f(x,y) and lim(x,y)-> (-∞,∞) f(x,y)?
sometimes it's easy but i don't know what to do with something like this 4a2 + 4a - 2ab + b2 +2 > 0
 
It's not always obvious how to demonstrate such a thing. It often requires some creativity. Try factoring. If you can find equivalent expressions that are perfect squares, this can be useful.
 
It's not always obvious how to demonstrate such a thing. It often requires some creativity. Try factoring. If you can find equivalent expressions that are perfect squares, this can be useful.

I know that in many cases you can use other methods, but I'm curious how to find limit of any two variable function.
 
Top