Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r 2 0, note that r →ot as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.)de-x2 - y2 - 4lim4e(x, y)→ (0, 0)x² + y2

Answered: Image /qna-images/answer/0dbef0cb-01f6-4f86-9cd7-e178b384debc.jpg

Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r2 0, note that r- 0+ as (x, y) - (0, 0).] (If an answer does not exist, enter DNE.) 4e-x2 - y2 - 4 x² + y2 lim (x, y)- (0, 0)

Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r2 0, note that r- 0+ as (x, y) - (0, 0).] (If an answer does not exist, enter DNE.) 4e-x2 - y2 - 4 x² + y2 lim (x, y)- (0, 0)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Concept explainers

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as:

Question

Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r 2 0, note that r →
ot as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.)
de-x2 - y2 - 4
lim
4e
(x, y)→ (0, 0)
x² + y2

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