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Consider the functions f(x, y) = sin¬' (9 – 2.0² – y²) and g(x, y) = x² – 4y². 1 %3D a. Identify and sketch the domain of f . b. Identify the level curve of the graph of g for each k e {-4,0, 4}. Sketch a contour map for the graph of g using these level curves.

Consider the functions f(x, y) = sin¬' (9 – 2.0² – y²) and g(x, y) = x² – 4y². 1 %3D a. Identify and sketch the domain of f . b. Identify the level curve of the graph of g for each k e {-4,0, 4}. Sketch a contour map for the graph of g using these level curves.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the functions f(x, y) = sin-' (9 – 2.x² – y?) and g(x, y) = x² – 4y². a. Identify and sketch the domain of f. b. Identify the level curve of the graph of g for each k e {-4,0, 4}. Sketch a contour map for the graph of g using these level curves. c. Discuss the continuity of the function h defined by f (x, y) g(x, y) if (x, y) E domf and g(x, y) # 0 h(x, y) = if (x, y) E domf and g(x, y) = 0 at the point (-2, 1). If discontinuous, identify the type of discontinuity.
Transcribed Image Text:1. Consider the functions f(x, y) = sin-' (9 – 2.x² – y?) and g(x, y) = x² – 4y². a. Identify and sketch the domain of f. b. Identify the level curve of the graph of g for each k e {-4,0, 4}. Sketch a contour map for the graph of g using these level curves. c. Discuss the continuity of the function h defined by f (x, y) g(x, y) if (x, y) E domf and g(x, y) # 0 h(x, y) = if (x, y) E domf and g(x, y) = 0 at the point (-2, 1). If discontinuous, identify the type of discontinuity.
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