# Limits with three variables (a different problem)

1. Oct 14, 2008

### physstudent1

1. The problem statement, all variables and given/known data

the limit as (x,y)->0,0 of (x^2+y^2)ln(x^2+y^2)
(Hint: as (x,y)->(0,0) r->0(from the right)

2. Relevant equations

3. The attempt at a solution

I converted to polar coordinates then used trig identities and eventually got to the limit of r->0(from theright) of r^2 * (ln(r^2)) I eventually got this limit to equal 0. I'm pretty sure to make sure the limit exists I have to evaluate it as r->0 (from the left) as well but I'm not sure how...

2. Oct 14, 2008

### nicksauce

You only need to evaluate the limit of r from one direction, as r is a variable that is always non-negative. Remember it represents a radius, ie a positive number.

3. Oct 14, 2008

### physstudent1

ohhhh I see thanks