A surface is defined by $$q(x,y) = \begin{cases} -\log_2\Bigl(\frac{1}{x^2+y^2-2} + 2\Bigr), &(x,y)\in D \\ 1, &(x,y) = (0,0) \end{cases}$$
Find D if q is over the maximal domain. I believe $$ D = {(x,y) \in \mathbb R^2 \mid x^2 + y^2 > \frac{9}{4} }$$
Do the level curves approach a limit as $$ q \rightarrow \infty $$
and if so, what is this limiting level curve.