How to prove for example that $\displaystyle \lim_{(x,y)\to(1,1)}(x^2+y^2)=2$ ?

Or $\displaystyle \lim_{(x,y)\to(0,1)}\frac{x+1}{y+1}=\frac12$ ?

I want to learn it. I've been looking for some notes that show how to prove multivariable limits by the epsilon-delta definition, but not succeed.