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Unformatted text preview: Name: MAC 2313 Exam 6 Version A 11/16/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero.  1. In the following problems if the angles are not exact, thats fine, just indicate the answer. a) Convert the point (2 , 4 , 1) from cylindrical to spherical coordinates. b) Convert the point (4 , 3 , 6 ) from spherical to rectangular coordinates.  2. Consider the integral I = Z 1 Z 1 x Z 1- y f ( x,y,z ) dzdydx . Switch the order of integration as indicated ***See picture in the book, section 15.6 problem 33*** a) Find bounds for the iterated integral so that I = R R R f ( x,y,z ) dzdxdy b) a) Find bounds for the iterated integral so that I = R R R f ( x,y,z ) dydxdz  3. (Example from class) Find the volume of the solid under the cone z 2 = 9 x 2 +9 y 2 and inside the cylinder x 2 + y 2 = 4, in the first quadrant find the volume of this solid above the xy-plane. [JUST SET UP]  4. Sketch the following (include appropriate labels) *If you drawing is too incomprehensible please describe 4....
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