This problem relates to the interpretation of div and curl given in the margin box just after their definition. Consider the four velocity fields F, G, H, and L, which have for every z the con-figuration illustrated in Figure 6. Determine each of the following by geometric reasoning.
(a) Is the divergence at p positive, negative, or zero?
(b) Will a paddle wheel with vertical axis at p (Figure 4, Section 14.7) rotate clockwise, counterclockwise, or not at all?
(c) Now suppose F = cj, G = e-y2j, H = e-x2j, and L = (xi + yj) / ˆšx2 + y2, which might be modeled as in figure calculate the divergence and curl for each of these fields and thereby confirm your answer in parts (a) and (b).

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АУ х н!