what is the limit of Sqrt[x^2 + y^2] as (x,y) approach (0,0)?
I wrote 0 on the exam but I realized it probably doesn't exist because the sqrt fcn is defined only for positive values of x and y, what do you guys think?
what is the limit of Sqrt[x^2 + y^2] as (x,y) approach (0,0)?
I wrote 0 on the exam but I realized it probably doesn't exist because the sqrt fcn is defined only for positive values of x and y, what do you guys think?
What you wrote on the exam is correct. If you look at the definition of a limit, it requires that "... for all $\displaystyle (x,y)$ in the domain of F with $\displaystyle 0<|(x,y)-(a,b)|<\delta$, $\displaystyle |F(x,y)-L|<\epsilon$."
So you don't need an $\displaystyle (x,y)$ that makes $\displaystyle F(x,y)$ negative, you just need to look to see what F does to $\displaystyle (x,y)$ pairs near the origin.
- Hollywood