Let (x, y) tan1 x y and u (2 2 , 2 2) (a) Calculate the gradient of f (b) Calculate Duf(1, 1) and Du(3, 1) (c) Show that the lines y mx for m 0 are level curves for f (d) Verify that Vfp is orthogonal to the level curve through P for P (x, y) (0,0) ...

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Let (x, y) = tan1 x/y and u = (2/2 , 2/2). (a) Calculate the gradient of

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Let ƒ(x, y) = tan−1 x/y and u = (√2/2 , √2/2).

(a) Calculate the gradient of f. (b) Calculate Duf(1, 1) and Du(3, 1). (c) Show that the lines y = mx for m #

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Let (x, y) = tan1 x/y and u = (2/2 , 2/2). (a) Calculate the gradient of

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(a) Calculate the gradient of f. (b) Calculate Duf(1, 1) and Du(3, 1). (c) Show that the lines y = mx for m # 0 are level curves for f. (d) Verify that Vfp is orthogonal to the level curve through P for P = (x, y) # (0,0).

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Calculus

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