1. The problem statement, all variables and given/known data Apply the definition of the limit to show that lim (x,y)-->(0,0) xy^3/(x^2+y^2) = 0 2. Relevant equations Definition of the limit: lim (x,y)-->(a,b) f(x,y) = L if for every number epsilon > 0 there is a corresponding number delta > 0 such that if (x,y) is in the domain and 0 < sqrt((x-a)^2 + (y-b)^2) < delta then |f(x,y) - L| < epsilon 3. The attempt at a solution So far I've just plugged in the numbers: Let epsilon > 0. We want to find delta > 0 such that if 0 < sqrt(x^2 + y^2) < delta then |xy^3/(x^2 + y^2) - 0| < epsilon I have no idea what to do next. Note that it says to show that this is the limit using the definition given above.