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Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the function k defined by f(x,y) k(x,y) = {g(x,y)' 0, if (x,y)e dom f and g(x,y) # 0 if (x,y)e dom f and g(x,y) = 0 at the point (-1,2) by answering the following questions: I. Does k(1,2) exist? I. Does lim (х,у)--(-1,2) k (х, у) еxist? I. Is lim k(x, y)equal to k(1,2)? (x,y)→(-1,2)

Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the function k defined by f(x,y) k(x,y) = {g(x,y)' 0, if (x,y)e dom f and g(x,y) # 0 if (x,y)e dom f and g(x,y) = 0 at the point (-1,2) by answering the following questions: I. Does k(1,2) exist? I. Does lim (х,у)--(-1,2) k (х, у) еxist? I. Is lim k(x, y)equal to k(1,2)? (x,y)→(-1,2)

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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Suppose f(x,y) = sin-1(6 – 2x2 – y2) and g(x,y) = 4x2 – y2.

Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the function k defined by f(x,y) k(x,y) = {g(x,y)' 0, if (x,y)e dom f and g(x,y) # 0 if (x,y)e dom f and g(x,y) = 0 at the point (-1,2) by answering the following questions: I. Does k(1,2) exist? I. Does lim (х,у)--(-1,2) k (х, у) еxist? I. Is lim k(x, y)equal to k(1,2)? (x,y)→(-1,2)
Transcribed Image Text:Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the function k defined by f(x,y) k(x,y) = {g(x,y)' 0, if (x,y)e dom f and g(x,y) # 0 if (x,y)e dom f and g(x,y) = 0 at the point (-1,2) by answering the following questions: I. Does k(1,2) exist? I. Does lim (х,у)--(-1,2) k (х, у) еxist? I. Is lim k(x, y)equal to k(1,2)? (x,y)→(-1,2)
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