If the following piecewise function is continuous

Question

If the following piecewise function is continuous, what is the value of $\alpha$

$
f(x,y)=
\begin{cases}
arctan(\dfrac{|x|+|y|}{x^2+y^2})&\text{if}\, (x,y)\ne(0,0)\\
\alpha&\text{if}\, (x,y)=(0,0)
\end{cases}
$

First I think I need to evaluate the limit of this function but I couldn't find the following limit

$$\lim\limits_{(x,y)\to(0,0)}arctan(\dfrac{|x|+|y|}{x^2+y^2}) $$

I checked this limit from wolfarm calculator but that says this limit does not exist.
So what can I do here ? please help

Answer 1

Hint: transform into polar coordinates, $x=r \cos \theta$ and $y = r \sin \theta$.