Obviously, you are right (thank you). Take ε=1. I can choose a point in the circle with radius \sqrt{2} that is not inside the square |x-1|+|y-1|<1.
How about this: if I choose a point inside the circle with radius ε, then that point is also inside the square with side 2ε, because the circle...
Actually I think I might have solved it:
I want to prove that
Given \epsilon> 0 there exist \delta> 0 such that if \sqrt{(x-1)^2+ (y-1)^2}<\delta then
\left|\frac{xy}{x+y}- \frac{1}{2}\right|<\epsilon
Now,
\left|\frac{xy}{x+y}-...
Hi,
I'm trying to wrap my head around epsilon/delta proofs for multivariable limits and it turns out I became stuck on an easy one!
The limit is:
\lim_{(x,y) \to (1,1)}\frac{xy}{x+y}
Obviously, the result is 1/2, but I'm unable to prove it!
Any hints?
Thank you!