Midterm2 - f ( x, y ) = xy in the region x 2 + y 2 1. 5....

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Math 2411 Mar 15, 2006 Honors Calculus III Spring 2006, Georgia Tech Midterm 2 Time: 50min 1. Find the center of mass of a half disk of radius 1. 2. Find the volume of the ellipsoid x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 ( Hint : Use a change of variables). 3. Find the average distance of a point in a ball of radius 1 from the center of the ball. 4. Find the maximum and minimum of
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Unformatted text preview: f ( x, y ) = xy in the region x 2 + y 2 1. 5. Show that for any three real numbers x , y , z , 3 xyz x + y + z 3 . ( Hint: Maximize x 2 y 2 z 2 subject to the constraint x 2 + y 2 + z 2 = a 2 ). Each problem is worth 20pts. Extra Credit: (5pts) Compute R - e-x 2 dx ....
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