1. The problem statement, all variables and given/known data Using the definition of a limit, prove that lim(x, y) --> (0,0) (x^2*y^2) / (x^2 + 2y^2) = 0 2. Relevant equations Now, I know that the limit of f(x, y) as (x, y) approaches (a, b) is L such that lim (x, y) --> (a, b) f(x, y) = L. Also, for every number epsilon > 0, there is a delta > 0 such that |f(x, y) - L| < epsilon. I believe the above is the definition of a limit of two variables. 3. The attempt at a solution In a sense, f(x, y) --> L (two VALUES) as (x, y) --> (a, b) (two POINTS). By making the distance between points (x, y) and (a, b) extremely small (some value epsilon), we make the distance between f(x, y) and L (some value delta) subsequently small. For any interval [L - epsilon, L + epsilon], there is a subsequent plane with center (a, b) and radius delta > 0 satisfying this. What I want to do is use some very small value of epsilon to find a value of delta that satisfies the definition of a limit.