In each of the following problems, plot the graph of f(x, y) and the corresponding gradient field F = (f on S = {(x, y)}; - 3 ( x ( 3, - 3 ( y ( 3}. In each case, curl F = 0 (Theorem 14.3D) and so there is no tendency for rotation around any point.
Let f(x, y) = x2 + y2.
(a) By visually examining the field F, convince yourself that div F > 0 on S. Then calculate div F.
(b) Calculate the flux of F across the boundary of S?