I'm trying to find $\displaystyle \displaystyle \lim_{(x,y)\rightarrow (0,0)} \frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1}$ which if it exists is obviously 2. I need an epsilon-delta argument but haven't made any progress. If I could find something like $\displaystyle x^{2}+y^{2} \leq \sqrt{x^{2}+y^{2}}$ that might help but this is false for small values.