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21. f(x, y) = x² - y²; P(-1, -3); 3 4 5 5 "

21. f(x, y) = x² - y²; P(-1, -3); 3 4 5 5 "

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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19. F(x, y) = e-²-2'; P(-1, 2) е 20. h(x, y) = ln (1 + x² + 2y²); P(2, -3) 21-30. Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. 21. f(x, y) = x² - y²; P(-1, -3); 22. f(x, y) = 3x² + y²; P(3, 2); y4 23. f(x, y) = 10 - 3x² + 4 x-y 3 4 5' 5 5 12 13 13 ; P(2, -3); √√3 2 1 2 5 12 13 13 1 2 √5' √5 24. g(x, y) = sin 7(2x - y); P(-1,-1); 25. f(x, y) = √√4 - x² – 2y; P(2,-2); 26. f(x, y) = 13ey; P(1, 0); (5, 12) 27. f(x, y) 3x² + 2y + 5; P(1, 2); (-3, 4) e-; P(In 2, In 3); (1, 1) 28. h(x, y) 29. g(x, y) = ln (4+x² + y²); g(-1, 2); (2, 1) ; P(4, 1); (1, 2) X 30. f(x, y) 31-36. Direction of steepest ascent and descent Consider the following functions and points P. a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find 2 vector that points in a direction of no change in the function at R 83°F Most
Transcribed Image Text:19. F(x, y) = e-²-2'; P(-1, 2) е 20. h(x, y) = ln (1 + x² + 2y²); P(2, -3) 21-30. Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. 21. f(x, y) = x² - y²; P(-1, -3); 22. f(x, y) = 3x² + y²; P(3, 2); y4 23. f(x, y) = 10 - 3x² + 4 x-y 3 4 5' 5 5 12 13 13 ; P(2, -3); √√3 2 1 2 5 12 13 13 1 2 √5' √5 24. g(x, y) = sin 7(2x - y); P(-1,-1); 25. f(x, y) = √√4 - x² – 2y; P(2,-2); 26. f(x, y) = 13ey; P(1, 0); (5, 12) 27. f(x, y) 3x² + 2y + 5; P(1, 2); (-3, 4) e-; P(In 2, In 3); (1, 1) 28. h(x, y) 29. g(x, y) = ln (4+x² + y²); g(-1, 2); (2, 1) ; P(4, 1); (1, 2) X 30. f(x, y) 31-36. Direction of steepest ascent and descent Consider the following functions and points P. a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find 2 vector that points in a direction of no change in the function at R 83°F Most
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