1. The problem statement, all variables and given/known data Find the limit, if it exists, or show that the limit does not exist: lim (x,y) -> (0,0) [(y^2*sin(x)^2)/(x^4+y^4)] (According to the textbook the limit 'does not exist') 3. The attempt at a solution Since the function is approaching the origin [(0,0)]: test path along y-axis: let x = 0 lim (y) -> (0) [0/y^4] = 0 test path along x-axis: let y = 0 lim (x) -> (0) [0/x^4] = 0 This is not efficient enough to prove that the limit is 0, therefore investigate further possibly using the squeeze theorem. I know that [(y^2)/(x^4+y^4)] <= 1 (but i don't know what to do with this information) 0 <= [(y^2*sin(x)^2)/(x^4+y^4)] <= ** ** Here is where i got stuck. I do not know what function fits the criteria and how to look for it. Please excuse me I just learned this theorem recently and I'm hoping someone can help me.