Limits

[wimma]

1. The problem statement, all variables and given/known data
A few:
(1) lim(x,y) -> (0,0) of (x^4*y^2)/(x^2 + y^2)2
(2) lim(x,y) -> (0,0) of x^4 / (y+x^2)

2. Relevant equations



3. The attempt at a solution
(1) i get that it exists and equals 0 by using polar coordinates
(2) i get that it exists (except for the parabolic path y=-x^2) and equals zero [using (t, mt) and (t, mt^2)]

[Dick]

1) looks fine. For 2) how can you have a limit 'except for' something? Look at the path x=t, y=(-t^2). Just because the limit exists on some paths doesn't prove anything.

[wimma]

yeah but the question says "please ignore the parabolic path y=-x^2" :)

[Dick]

Since the denominator vanishes on that path, what do you think happens very close to that path?