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.)

Question

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)

Steve · Accepted Answer

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