Solved: PROJECT. Useful Formulas for the Divergence. Prove

Chapter 9, Problem 9.1.261

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PROJECT. Useful Formulas for the Divergence. Prove (a) div (kv) = k div v (k constant) (b) div(fv) = fdi\'v + vo"\f (c) div (f\g) = f\2g + '\fo'\g(d) div (f'\ g) - div (gV f) = fV2g - g,\2f.Verify (b) for f = eX1JZ and v = ad + byj + c:::k.Obtain the answer to Prob. 4 from (b). Verify (c) forf = x 2 - y2 and g = eX + Y. Give examples of your ownfor which (a)-(d) are advantageous.

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