MAC 2313 Midterm: MAC2313 S15 Test 4
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Some answers will involve square roots, fractions, logarithms, , 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. ) Find the following, for the three points a, b, and c: C = (0, 1, 1) (a) find the equation of the plane that passes through a, b and c. (b) find the area of the triangle with vertices a, b and c. (2) (30 pts. ) For the parametric space curve c de ned by r(t) = (cid:10)tet, 2t + 1, 3et(cid:11) , For the function f (x, y) = x2 8x(y2 y) Classify each critical point as a local maximum, local minimum or saddle point. (5) (20 pts. ) Let c be the triangle in the (x, y)-plane with vertices (0, 0), (2, 0), and (2, 1).
