Another method for computing limits as (x, y) → (0,0) is to convert to polar coordinates: substitute x =r cos 0, y = r sin 0, and compute the limit as r → 0.If the limit as r → 0 exists, then so does the limit at (x, y) → (0, 0), and both limits are equal.If the value of the limit as r → 0 depends on 0, then the limit as (x, y) → (0,0) does not exist.Find the limits. Enter "DNE" if the limit does not exist.- ylim(x,y)→(0,0)cosx2 + y24xlim(x,y)→(0,0) x2 + 3y+ y²

Find the limits : Given : lim(x,y)→(0,0)cosx7-y7x2+y2 = cos 0-00+0…

Answered: Find the limits. Enter "DNE" if the…

Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim (х.)-(0,0) х2 + Зу+ у? =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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

Another method for computing limits as (x, y) → (0,0) is to convert to polar coordinates: substitute x =r cos 0, y = r sin 0, and compute the limit as r → 0.
If the limit as r → 0 exists, then so does the limit at (x, y) → (0, 0), and both limits are equal.
If the value of the limit as r → 0 depends on 0, then the limit as (x, y) → (0,0) does not exist.
Find the limits. Enter "DNE" if the limit does not exist.
- y
lim
(x,y)→(0,0)
cos
x2 + y2
4x
lim
(x,y)→(0,0) x2 + 3y+ y²

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