MAC 2313 Midterm: MAC2313 F13 Test 4
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Some answers will involve square roots, fractions, , e, et cetera. Unless speci ed otherwise, always assume up means in the z-direction, and positive orientation is with respect to the right-hand rule. (1) (15 pts. ) For the parametric space curve c de ned by. 2 r(t) = hcos t, sin t, ti , 0 t answer the following. (a) find r (t). (b) find the length of c. (c) evaluate the line integral zc xdx + ydy + xydz. (3) (30 pts. ) Let p0 = (1, 1), v = h2, 3i, and f (x, y) = x y. For the function f (x, y) = (y 1 + x2)y. Classify each critical point as a local maximum, local minimum or saddle point. (5) (15 pts. ) Use the method of lagrange to minimize the function subject to the constraint f (x, y) = x2 + (y 6)2 x2 y2 = 1.
