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.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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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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