2. Consider the following two functions: = f(x, y) = (x – 2y), = g(x, y) = (x – 2y)². = Z (a) Give the level curves for both f and g consisting of the (z = 0,1,2, 3)-values. Label each level curve with the respective z value. (b) Let S be the graph of f and let T be the graph of g. Turn your two level curve diagrams in part (a) into separate sketches of S and T in three-dimensional coordinate system by plotting the level curves at the appropriate altitude. (c) Both S and T are examples of one of our familiar named surfaces. Use their defining equations and your sketches in part (b) to identify which.
2. Consider the following two functions: = f(x, y) = (x – 2y), = g(x, y) = (x – 2y)². = Z (a) Give the level curves for both f and g consisting of the (z = 0,1,2, 3)-values. Label each level curve with the respective z value. (b) Let S be the graph of f and let T be the graph of g. Turn your two level curve diagrams in part (a) into separate sketches of S and T in three-dimensional coordinate system by plotting the level curves at the appropriate altitude. (c) Both S and T are examples of one of our familiar named surfaces. Use their defining equations and your sketches in part (b) to identify which.
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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![2. Consider the following two functions:
z = f(x, y) = (x – 2y),
z = g(x, y) = (r – 2y)?.
(a) Give the level curves for both f and g consisting of the (z = 0,1, 2, 3)-values. Label each
level curve with the respective z value.
(b) Let S be the graph of f and let T be the graph of g. Turn your two level curve diagrams in
part (a) into separate sketches of S and T in three-dimensional coordinate system by plotting
the level curves at the appropriate altitude.
(c) Both S and T are examples of one of our familiar named surfaces. Use their defining equations
and your sketches in part (b) to identify which.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F153f7311-79ea-4d70-a40c-822c1ada8bcd%2Ff38e64b3-9131-4a8c-94b7-3aaac49e7142%2Fsuj5o7_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the following two functions:
z = f(x, y) = (x – 2y),
z = g(x, y) = (r – 2y)?.
(a) Give the level curves for both f and g consisting of the (z = 0,1, 2, 3)-values. Label each
level curve with the respective z value.
(b) Let S be the graph of f and let T be the graph of g. Turn your two level curve diagrams in
part (a) into separate sketches of S and T in three-dimensional coordinate system by plotting
the level curves at the appropriate altitude.
(c) Both S and T are examples of one of our familiar named surfaces. Use their defining equations
and your sketches in part (b) to identify which.
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