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) 9e−x2 − y2 − 9 x2 + y2

Answer 1

complete question is:

Use polar coordinates to find the limit. [If (r, theta) are polar coordinates of the point (x,y) with r>=0, note that r tends to 0+ as (x,y) tends to (0,0).] lim (x,y) tends to (0,0) x^3+y^3/x^2+y^2

Answer:

0

Step-by-step explanation:

$\lim_{(x,y) \to \(0,0)} \frac{x^3+y^3}{x^2+y^2}\\ \lim_{r \to 0} \frac{x^3(cos^3theta+sin^3theta)}{r^2}\\\\\lim_{r \to 0}r(cos^3theta+sin^3theta)\\=0$