I calculated the iterated limits of the function. They are -1 and 1. Since the limits are not the same, does that prove that the function is not continuous at (0,0)? Or do i have to do more stuff?
$f(x,y) = \begin{cases}\frac {x^2-y^2}{x^2+y^2}&(x,y)\neq (0,0)\\k& (x,y)=(0,0)\end{cases}$
Also, there's another exercise where they give k=1 and ask to calculate the partial derivative in x at (0,0). Why do I need k=1?
The function $$f(x,y) = \begin{cases}\frac {x^2-y^2}{x^2+y^2}&(x,y)\neq (0,0)\\k& (x,y)=(0,0)\end{cases}$$
is not continuous at $(0,0)$ because the limit does not exist at that point.
You have shown this fact by approaching $(0,0)$ from different directions and having different limits.
For partial derivative you need the value of your function at $(0,0)$ to find the limit of the difference quotient so they gave you $k=1$ to use it in order to find the partial derivative.