Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
8. The temperature in °C on the surface of a metal plate is given by T(x, y)= 20-4x² - y² , where x and y %3D are measured in inches. a) In what direction from (2,-3) does the temperature increase most rapidly? What is this rate of increase? b) Provide a contour map and draw the vector that indicates the direction of most rapid increase at (2,-3). c) What is the hottest point on the plate? Note that the vector does not point toward the hottest point on the plate. That is because the gradient provides only a local solution to finding a maximum increase.
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Transcribed Image Text:8. The temperature in °C on the surface of a metal plate is given by T(x, y)= 20-4x² - y² , where x and y %3D are measured in inches. a) In what direction from (2,-3) does the temperature increase most rapidly? What is this rate of increase? b) Provide a contour map and draw the vector that indicates the direction of most rapid increase at (2,-3). c) What is the hottest point on the plate? Note that the vector does not point toward the hottest point on the plate. That is because the gradient provides only a local solution to finding a maximum increase.
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