MATH 215 Final: finalw15
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Winter 2015, math 215 calculus iii, final exam. Let s be the boundary surface of solid: let ~f (x, y, z) be the vector eld. ~f (x, y, z) = xy2~i + yz2 ~j + zx2 ~k. ~f d~s: (10 points) let c be the part of the circle x2 + y2 = 1 from point (1, 0) to point ( 1. Hence it is a 1/8th of the circle and is oriented in the counter-clockwise direction. ~f (x, y) = hy cos(xy) + y, x cos(xy) + xi. Answer the following two questions in yes or no. No need to explain. (a) (3 points) suppose that f (x, y) is a function with continuous derivatives and (x0, y0) is a local maximum of f . Then, is it true that all directional derivatives d~uf (x0, y0) at (x0, y0) are zero for arbitrary unit vector ~u? (b) (3 points) let f (x, y) be a function with continuous derivatives.
