Here you can convert to polars...
I agree that you can bound this function with
.
Now to squeeze the function, you need to evaluate which you can do by converting to polars...
.
I need to find:
lim as (x,y) => (0,0) of ((x - y)^2) / (abs(x) + abs(y))
I know that the limit should be 0, and I am searching for a bounding function B(x) to use the squeeze theorem with.
I have so far:
0 <= abs[f(x,y) - L] = abs[((x - y)^2) / (abs(x) + abs(y))]
<= ((x - y)^2) / abs(x + y)
dropping the absolute value bars since all terms are positive, and combining abs(x) and abs(y) using the triangle inequality
Where can I go from here to remove the denominator and find a bounding function?