MATH 231 Final: Math 231 Fall2013FinalExam
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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. You must show your work on all problems to receive full credit. Please be sure to box your nal answers for full credit. Explain your answer: which shaded region best describes the domain of f (x, y) := ln(y2. 4 y2 ? (a) graph1 (c) graph4 y y (b) graph2 x x y y (d) graph3 x x: (5pts) let v and w be three-dimensional vectors, and assume that neither of them are equal to 0. 2 (a) 1 (b) 1 (c) 3 (d) 0 (e) none of the above: (5pts) let f (x, y, z) = x y+2z . Then fyz(3, 1, 1) is: (a) 2/27 (b) 2/9 (c) 4/9 (d) 4/9 (e) none of the above: (5pts) let f (x, y) := e5 x2.
