Question

Can't figure out how to do the delta-epsilon limit proof for this...

Answer 1

\[\lim_{(x, y) \rightarrow (0, 0)} \frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1} = 2\]

Answer 2

My two statements for the proof are:\[0 < \sqrt{x^{2}+y^{2}}< \delta \]and\[\left|\frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1} \right| < \epsilon \] but I can't figure out how to finish the proof...

Answer 3

is it not |f(x)-L| were L=2 f(x) is ur function?

Answer 4

Sorry, I forgot to put that in there...it's on my paper though

Answer 5

\[\left|\frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1}-2 \right| < \epsilon \]