1. The problem statement, all variables and given/known data Let f(x,y) be defined : f(x,y) = 0 for all (x,y) unless x4 < y < x2 f(x,y) = 1 for all (x,y) where x4 < y < x2 Show that f(x,y) → 0 as (x,y) → 0 on any straight line through (0,0). Determine if lim f(x,y) exists as (x,y) → (0,0). 2. Relevant equations Polar co - ordinates maybe? 3. The attempt at a solution Pretty confused with this one actually. Not sure where to start. I want to show f(x,y) → 0 as (x,y) → 0 on any straight line through the origin. So would I pick lets say y=x. Then f(x,x) = I'm not sure, having trouble with the inequalities.