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234-slemrod-08faex02

# 234-slemrod-08faex02 - Math 234 M Slemrod Exam 2 NAME...

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Unformatted text preview: Math 234 M. Slemrod Exam 2 November 20, 2008 NAME: TA’s NAME: Closed book, no notes, calculators, books, electronic devices of any kind (e.g. MP players). ' SHOW ALL YOUR WORK! Math 234 Page 1 1. Compute the volume of region D that lies inside the cardoid 7” 2 2 + sin (9, outside the circle 7“ = 2, above the xy—plane, and below the plane 2 = 4. Hint: Useful formula 1 \$1112 6 = 5(1 — cos 20) Answer: (33 pts) Math 234 Page 2 2. Use integration to ﬁnd the volume of the tetrahedron in the ﬁrst octant (x Z O, y 2 0, 2 Z O) bounded by the coordinate planes passing through (1, 0,0), (0, 2, 0), (0, 0, 3). Answer: (33 pts) Math 234 , Page 3 3. Use Lagrange multipliers to ﬁnd the largest product Cf three positive numbers :13, y, z satisfying :1: + y + 22 : 20. Answer: (34 pts) ...
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234-slemrod-08faex02 - Math 234 M Slemrod Exam 2 NAME...

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