ex6_fall11_2313

ex6_fall11_2313 - Name MAC 2313 Exam 6 Version A SHOW ALL...

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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. [6] 1. In the following problems if the angles are not exact, that’s fine, just indicate the answer. a) Convert the point (2 , π 4 , 1) from cylindrical to spherical coordinates. b) Convert the point (4 , π 3 , π 6 ) from spherical to rectangular coordinates. [6] 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 [6] 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] [6] 4. Sketch the following (include appropriate labels) *If you drawing is too incomprehensible please describe[6] 4....
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ex6_fall11_2313 - Name MAC 2313 Exam 6 Version A SHOW ALL...

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