(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit problem

**Physics Forums | Science Articles, Homework Help, Discussion**