Answer
limit $l$ does not exist
Work Step by Step
Consider $l=\lim\limits_{(x,y) \to (0,0)} \dfrac{x^2+y^2}{xy}$
Suppose $y=p x$; $p \ne 0$
Now, $l=\lim\limits_{(x,px) \to (0,0)} \dfrac{x^2+p^2 x^2}{px^2}$
Hence, $l=\lim\limits_{(x,px) \to (0,0)} \dfrac{1+p^2}{p}=\dfrac{1+p^2}{p}$
Hence, the limit $l$ does not exist as we can see that $l$ will have different limits for different values of $p$.
