I would switch to polar coordinates and find the limit as r goes to zero.
Can anyone guide me as to how I would evaluate this limit
lim as (x,y) -> (0,0) of ( (x^2 + y^2)^(1/2) x ln(1/(x^2 + y^2)^(1/2))
i plugged in several paths and the limit was 0 for all of them but I am required to do it the delta epsilon way