MATH 231 Final: Math 231 Spring2012FinalExam
Document Summary
The use of a calculator, cell phone, or any other electronic device is not permitted in this examination. The use of notes of any kind is not permitted during this exam. Work is required on all problems for full credit, with the exception of questions 1-8. Please be sure to box your nal answers for full credit. Then fy(x, y) evaluated at (2, 0) is (a) 2e 1 (b) 2 (c) e 1 (d) 0. 2: (5 points) suppose a b = 6 2, |a| = 4, |b| = 3. Then |a b| = (a) 6 (b) 6 2 (c) 2 3/3 (d) 3 2: (5 points) let f (x, y, z) = 2x2 + y2 z2 6z. Then the level surfaces of f are always (a) hyperboloids. (b) hyperboloids or a cone. (c) elliptic paraboloids. (d) hyperbolic paraboloids. (e) ellipsoids or a point. (f) none of the above. 3: (5 points) suppose x2z + yz3 = xy.
