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30. Let f(x, y) (x - y) (x + y) for which Find the directions u and the values c

30. Let f(x, y) (x - y) (x + y) for which Find the directions u and the values c

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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30. Let f(x, y) Find the directions u and the values of (x + y) D.f for which a. D,fi is largest b. D.f is smallest c. D.f D. d. D.f e. D. 22 31. Zero directional derivative In what direction is the derivative of fx yl- y +yat P3, 2) oqual to zero? 32. Zero directional derivative In what directions is the dervative of fix v) = (x -y/G+y}at PO. ) equal to zero? 33. Is there a direction u in which the rate of changec of ftr, y) r=3y +4y at AI, 2) equals 147 Grve reasons for your answer. 34. Changing temperature along a circle Is there a direction u in which the rate of change of the temperature function /ix, 2 2xyy (temperature in degrees Celsius, distance in feet) at P(1.-1. 1) is-3°C/1? Give reasons for your answer. 35. The derivative of f(x, ) at P(1.2y in the direction of i + is 2/2 and in the direction of-2j is--3. What is the derivative of fin the direction of-i- 2j? Give reasons for vour answer. meet.googie.com is shanng your screen.
Transcribed Image Text:30. Let f(x, y) Find the directions u and the values of (x + y) D.f for which a. D,fi is largest b. D.f is smallest c. D.f D. d. D.f e. D. 22 31. Zero directional derivative In what direction is the derivative of fx yl- y +yat P3, 2) oqual to zero? 32. Zero directional derivative In what directions is the dervative of fix v) = (x -y/G+y}at PO. ) equal to zero? 33. Is there a direction u in which the rate of changec of ftr, y) r=3y +4y at AI, 2) equals 147 Grve reasons for your answer. 34. Changing temperature along a circle Is there a direction u in which the rate of change of the temperature function /ix, 2 2xyy (temperature in degrees Celsius, distance in feet) at P(1.-1. 1) is-3°C/1? Give reasons for your answer. 35. The derivative of f(x, ) at P(1.2y in the direction of i + is 2/2 and in the direction of-2j is--3. What is the derivative of fin the direction of-i- 2j? Give reasons for vour answer. meet.googie.com is shanng your screen.
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