Question: Determine wether a-f is true or false (a) div (curl F) = 0 for any C2 vector field F. (b) Let F(x, y) = yi

Determine wether a-f is true or false

(a) div (curl F) = 0 for any C2 vector field F. (b) Let F(x, y) = yi + 2xy j and let C be the circle x2 + y2 = 1, oriented clockwise. Then F . ds = - 27. (c) V . (Vf) = 0 for any C2 function f on R3. (d) Let S be a sphere. For any C2-vector field F on R3 we have ff curl F . ds = 0. (e) Assume that S is obtained by revolving the graph of y = f(x) with a

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