edit: nvm what i just said.
polar coordinate that Twig showed is the way to go. It drops you down from two variables (x, y) to one (r).
It tells me there is no limit at the origin since there are points close to the origin which the function takes the value 1/2 and not 0 ?
Why use polar coordinates on the first one?
Also, are there any pointers you can advise on how to approach these questions, i.e. finding the value of a limit at a point(for vector valued fns)?
I used polar coordinates because I find it convenient and relatively easy here to show that no matter what angle we approach by, the function tends to zero.
I´m not that familiar with vector valued functions to be honest, I have only done these types of limits when .
But I would imagnine that both limits have to exist for a vector to approach some point so to speak.