If all of the contours of a function gxy (, ) are parallel lines, then the funct

Question

If all of the contours of a function gxy (, ) are parallel lines, then the function must be linear.

45. True or False? (a) If all of the contours of a function g(x, are parallel lines, then the function must be linear. (b) If curl F is parallel to the x-axis for all x, y, and z and if C is a circle in the x-plane, then the circulation of F around C must be zero. (c) If f is a differentiable function, then f(a,b) Vf (a, b) (d If F is a divergence free vector field defined everywhere and S is a closed surface oriented inward, then F.dA-o. (e) If G is a curl free vector field defined everywhere and C is a simple closed path, then G.dr 0.

Explanation / Answer

a> True

Since the slope is independent of how many of times we change the x and the y variables

, this slope remains constant over the whole contour map; thus, the

contours are all parallel straight lines.

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