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- 8x2 5x2 + 5y2 if (x, y) # (0, 0); Consider the function f(x, y): if (x, y) = (0, 0).

- 8x2 5x2 + 5y2 if (x, y) # (0, 0); Consider the function f(x, y): if (x, y) = (0, 0).

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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- 8x? 5æ2 + 5y2 if (x, y) + (0,0); Consider the function f(x, y) if (ӕ, у) —D (0, 0). 1. As (x, y) → (0, 0) along the x-axis, lim (x , y) → (0,0) f(x, y) 2. As (x, y) → (0, 0) along the line y = x, lim (x , y) → (0,0) f(x, y) 3. Given your answers above, which of the following statements are true? (Select more than one if appropriate.) O f(x, y) is continuous at (0, 0). O f(x, y) has a limit at (0, 0). O f(x, y) is not continuous at (0, 0). O f(x, y) does not have a limit at (0, 0). O More information is needed to conclude something about the limit or continuity of f(x, y) at (0, 0).
Transcribed Image Text:- 8x? 5æ2 + 5y2 if (x, y) + (0,0); Consider the function f(x, y) if (ӕ, у) —D (0, 0). 1. As (x, y) → (0, 0) along the x-axis, lim (x , y) → (0,0) f(x, y) 2. As (x, y) → (0, 0) along the line y = x, lim (x , y) → (0,0) f(x, y) 3. Given your answers above, which of the following statements are true? (Select more than one if appropriate.) O f(x, y) is continuous at (0, 0). O f(x, y) has a limit at (0, 0). O f(x, y) is not continuous at (0, 0). O f(x, y) does not have a limit at (0, 0). O More information is needed to conclude something about the limit or continuity of f(x, y) at (0, 0).
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