MATH 234 Final: Math 234 Winter 2012 Final
15 Feb 2019
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Instructions: read each problem carefully, write legibly, show all of your work on these sheets, the exam consists of 10 problems and 11 pages. Please verify that you have all 11 pages: you may not use books, notes or calculators, you have 120 minutes to complete this exam. Double-angle formula: cos2 = sin2 = Page 2 of 11: in evaluating a double integral over a region d, a sum of iterated integrals was obtained as follows. 2 f (x, y) dx dy +z 0. Y2 f (x, y) dx dy. (a) sketch the region d of integration. (b) express the double integral as one iterated integral with reversed order of integration. Page 3 of 11: evaluate the triple integral. Zzzd y2 dv where d is the solid region bounded by the parabolic cylinder z = 1 y2, and the planes x + 2z = 2, x = 0, and z = 0.
