1. The problem statement, all variables and given/known data The function exp[ (x2 + y2 - xy)/(x2 + y2) ] = f(x,y) is continuous on the open first quadrant. Prove it is bounded there. Prove f cannot be extended continuously to the closed first quadrant. 3. The attempt at a solution Since f is a real-valued function defined and continuous on a compact set (open first quadrant...I think...), then f is bounded..? So I have to show that the open first quadrant is a compact set maybe? I think I have to show that f is not uniformly continuous on the closed first quadrant. So, there exists an epsilon > 0 where a number d >0 cannot be found such that |f(p) - f(q)| < epsilon whenever p and q are in the closed first quadrant and |p-q|<d. I have so much trouble starting my proofs properly. I don't know how to set them up at the beginning, even when I know the rough outline.