To prove the limit exists $lim_{x,y \to (0,0)} \frac{e^{-(x^2+y^2)}-1}{x^2+y^2}$

Question

I want to prove the limit exists without the use of polar coordinates. I was asked to it by delta-epsilon method. However since it has $e^{-x^2+y^2}$ I can't seem to do it since I only know to do it with polinomials in fractions.

Thank you all so much.