Question: 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).

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 #

(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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