is the next function countnius at (0,0) ? + teoratical question

is the next function countnius at (0,0) ? + teoratical question

Hi I have problem to decide if

is continuous at (0,0).
I have tried to slove this by polar cordinates

but from here the only thing I can tell is , that for every teta, the
limit will be 0.
Is it Enough? because it seems to me that in this case I am only showing
that for every linear path to (0,0) the limit will be 0 ? and is this
function really continuous?
one more thing I heard about a Rule of thumb that if the sum of the powers
in the numerator is lower then the denominator the limit doesn't exist. is
it allways true? thanks,