1. does the limit (x+y)/(x^2-y^2) as (x,y) goes to (0,0) exist? If yes, find it. If no, show that it doesn't exist.
= (x+y)/(x+y)(x-y)=1/(x-y). Doesn't exist. It can cancel as long as not at (0,0), and this is undefined. (I think I did this right, but can you give me an alternative reason?)
2. Limit of x^2/y^2 as (x,y) goes to (0,0). Does it exist?