Question A$1(3$ marks$)$

Given the function

$f(x,y)=\frac{x^2-y^2}{x^2+y^2},(x,y)(0,0)$

determine whether $f(x,y)$ is continuous at $(0,0)$ by evaluating its limit along the following paths: $y=0,y=x,y=2x$ and $y=x^2.$