Ant_on_a_Heated_Plate - Ant on a Heated Plate: A ant is...

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Unformatted text preview: Ant on a Heated Plate: A ant is confined to walk in a circle of radius 5 about the origin on a heated plate with the following temp profile T ( x, y ) = 4 x 2 − kxy + y 2 . Determine the temperature extrema the ant will encounter for k = 4. 6 150 0.1 0.1 25 5 10 50 150 125 100 350 125 100 50 25 4 250 2 200 175 0.1 0.1 25 5 125 100 z 150 y 0 50 25 10 100 -2 50 175 50 0.1 0.1 -4 0 5 10 25 10 -50 6 4 2 0 y -2 -4 -10 -6 -5 0 x 5 10 -6 -6 -4 -2 0 x 50 25 5 5 10 2 4 k=4 Critical pt at origin leaves 2nd partials test inconclusive 6 175 150 125 10 0.1 -5 -1 0 -5 400 100 25 0-2 .1 10 5 4 350 -2 300 50 2 250 150 125 10 y 100 -2 50 50 10 0.1 25 0 10 -50 6 4 2 0 0 y -2 -4 -6 -10 x -4 -2 -5 -2 5 50 25 5 150 -6 -6 -4 -2 0 x 2 150 125 175 -5 0.1 10 25 100 5 4 150 125 0 100 25 200 z 0.1 5 0.1 10 100 50 25 5 6 k = 5 Critical pt at origin transitioned to a saddle pt. 125 100 50 300 10 5 6 -10 6 150 50 300 25 4 250 175 125 100 10 10 25 50 5 5 2 200 50 50 z 100 100 10 10 -2 125 25 150 25 0.1 y 0 100 10 50 50 50 -4 25 0 6 25 10 4 2 0 0 y -2 -4 -6 -10 x -6 -6 -4 -2 0 x 2 150 125 4 175 125 k = 3 Critical pt at origin is now a local minimum 100 5 6 ...
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This note was uploaded on 12/25/2009 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

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