I am given the limit :
$$ \lim_{(x,y)\to (0,0)}\left[ \ x^2 + y^2 \ln(x^2+y^2)\right] $$
to solve using polar coordinates first I would convert the equation to polar coordinates : $$ \lim_{(x,y)\to (0,0)} \left[\sin^2(\theta) + \cos^2(\theta) \ln(\sin^2(\theta) + \cos^2(\theta)) \right]$$
can I apply substitution to get:
$$ \ln(1) = 0$$