# Epsilon-Delta Argument for a Function in Two Variables

• Feb 27th 2011, 07:14 PM
ragnar
Epsilon-Delta Argument for a Function in Two Variables
I'm trying to find $\displaystyle \lim_{(x,y)\rightarrow (0,0)} \frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1}$ 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 $x^{2}+y^{2} \leq \sqrt{x^{2}+y^{2}}$ that might help but this is false for small values.
• Feb 27th 2011, 07:39 PM
TKHunny
Have you considered a substitution? W = x^2 + y^2.
• Feb 27th 2011, 07:54 PM
ragnar
I solved it. The result is trivial when you switch to polar coordinates.