It is part of my HW, I solved it and got that the following limit is 2, But Wolfram says that the limit does not exists \ path dependent. After few hours of trying to find a path to dismiss the limit I came up with nothing..
Would appreciate any help (sorry in advance for not writing it nicely xD )
$\lim_ {(x,y) \rightarrow(0,0)} \frac{\ln(1+2x^2+4y^2)}{\arctan(x^2+2y^2)}$