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Math Help - Epsilon-Delta Argument for a Function in Two Variables

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    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.
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    Have you considered a substitution? W = x^2 + y^2.
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    I solved it. The result is trivial when you switch to polar coordinates.
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