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2д. 2.1 x² + y? Examine the behavior of f(x, y) as (x, y) approaches (0, 0). (a) Changing to polar coordinates, we find 2x2.1 lim (x,y)→(0,0) \ x2 + y? lim r→0+, 0=anything (1)=0 Use "theta" for 0. Use "infinity" for "o" and "-infinity" for "-oo". Use "DNE" for "Does not exist". (b) Since f(0, 0) is undefined, f has a discontinuity at (x, y) = such that g(x, y) = f(x,y) for all (æ, y) + (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. = (0,0). Is it possible to define a function g : R² → R

2д. 2.1 x² + y? Examine the behavior of f(x, y) as (x, y) approaches (0, 0). (a) Changing to polar coordinates, we find 2x2.1 lim (x,y)→(0,0) \ x2 + y? lim r→0+, 0=anything (1)=0 Use "theta" for 0. Use "infinity" for "o" and "-infinity" for "-oo". Use "DNE" for "Does not exist". (b) Since f(0, 0) is undefined, f has a discontinuity at (x, y) = such that g(x, y) = f(x,y) for all (æ, y) + (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. = (0,0). Is it possible to define a function g : R² → R

Calculus: Early Transcendentals
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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11.1 11.2: Problem 4 2x2.1 Examine the behavior of f(x, y) as (x, y) x² + y? approaches (0, 0). (a) Changing to polar coordinates, we find (1) = 2x2.1 lim (x,y)→(0,0) ) x² + y? lim r→0+, 0=anything 0 Use "theta" for 0. Use "infinity" for "o" and "-infinity" for "-∞". Use "DNE" for "Does not exist". (b) Since f(0,0) is undefined, f has a discontinuity at (x, y) = (0,0). Is it possible to define a function g : R² → R such that g(x, y) = f(x,y) for all (x, y) # (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. g(0,0) =
Transcribed Image Text:11.1 11.2: Problem 4 2x2.1 Examine the behavior of f(x, y) as (x, y) x² + y? approaches (0, 0). (a) Changing to polar coordinates, we find (1) = 2x2.1 lim (x,y)→(0,0) ) x² + y? lim r→0+, 0=anything 0 Use "theta" for 0. Use "infinity" for "o" and "-infinity" for "-∞". Use "DNE" for "Does not exist". (b) Since f(0,0) is undefined, f has a discontinuity at (x, y) = (0,0). Is it possible to define a function g : R² → R such that g(x, y) = f(x,y) for all (x, y) # (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. g(0,0) =
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