use polar coordinates and L'hopital's rule to find the limit:
Lim (x,y) -> (0,0) of (x2 + y2)*ln(x2+y2)
The Attempt at a Solution
I was told in class we couldn't use l'hopital because of the multivariable thing, and I was also told the coordinate switch from rectangular to polar wasn't possible. I'm not sure if the problem is a trick question, because if I can't use L'hopital I would say the limit doesn't exist at (0,0) but how am i supposed to do this before the ideas of partial derivatives are introduced? How am I supposed to use L'Hopital's rule to help that is.
and when do I use the polar switch? before or after I take L'Hopital?
when I do switch over to polar should (x,y) become (rcos(θ),rsin(θ)) -> (0,0) or do I have to switch over from (0,0) to some other angle? am I picking an angle that simultaneously makes cos and sin zero? I don't think that one is possible, so perhaps I switch to something like (pi/2, pi) or (0,2pi) how do I choose between those? I could see sign errors arising if I make the wrong choice.
Thank you for your time.