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3. (Extra credit). Let f and g be functions, let C' be a curve and let S be a surface. Prove the following identities. If you appeal to theorems, state which of the hypotheses of those theorems you are assuming to be true. (a) (fVg) . dr = (Vf x Vg) . ds C S (b ) ( fvf ) . dr = 0 C (c) ( (f Vg + gVf) . dr =0 C