1. The problem statement, all variables and given/known data 2. Relevant equations lim(x,y)->(a,b)f(x,y) continuous at (a,b) if lim(x,y)->(a,b)f(x,y)=f(a,b) Squeeze theorem if lim a=lim c and lim a<= lim b <= lim c then lim b= lim c 3. The attempt at a solution I proved that all the limits exist but somewhat the functions aren't all continuous. I don't know what I did wrong but the answer I submitted (all continuous) is wrong. 1) using the squeeze theorem on the absolute value of g(x,y) i get 0<= 8x^2y^2/(x^2+y^2) <=8y^2 (since x^2/(x^2+y^2)<1) so the limit at (0,0) is equal to 0, which is also equal to f(0,0), hence the function is continuous 2)I used the squeeze theorem once again and replaced x^3/(x^2+y^2) and am left with limit of 7xsiny which gives 0 so it is continuous 3) I expressed the limit as a substration of two limits, and using the squeeze theorem on each of them got 0. I once again used x^2/(x^2+y^2)<1 and y^2/(x^2+y^2)<1 to get limit of xy - limit of 9y^2 which both equal to 0. 4) using the squeeze theorem and the fact that x^2/(x^2+y^2)<1, I get limit of 6y which equals 0 5) Same as 3 In theory I proved that all the limits exist and are equal to 0 so all the function should be continuous. Does anyone have any clue regarding what I did wrong? Thanks!