calc 3
posted by Becky on .
Use polar coordinates to find the limit. [If (r, θ) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.)
lim (x, y)→(0, 0) [(3e^−x^2− y^2) − 3]/
(x^2 + y^2)

in polar coordinates, we have
lim (r>0) (3e^(r^2)3)/r^2
= lim 6re^(r^2))/2r
= lim 6e^(r^2)/2
as r> 0, lim = 3