MATH 234 Midterm: Math 234 Spring 2013 Test 1
15 Feb 2019
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Instructions: mark your section, read each problem carefully, write legibly, show all of your work on these sheets, the exam consists of 5 problems and 6 pages. Please verify that you have all 6 pages: you may not use books, notes or calculators, you have 60 minutes to complete this exam. Page 2 of 6: (10 points) evaluate the double integral. 9px2 + y2 dy dx by converting to polar coordinates. Page 3 of 6: (10 points) evaluate the triple integral. Page 4 of 6: (10 points) evaluate the triple integral. 1 x2 + y2 + z2 dv using spherical coordinates, where d is the solid region that lies above the plane z = 3 and below the sphere x2 + y2 + z2 = 4z. Page 5 of 6: (10 points) use the change of variables u = 3x + y, v = y to compute the double integral.
