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Unformatted text preview: MAC 2313, Fall 2010 — Midterm 4 Review Problems 1 We will discuss these problems in class on Monday 11/15. Solutions will be posted on the course webpage over the weekend. 1 A bounded region in the first octant of 3dimensional Euclidean space has the surface x + y + z 2 = 1 as part of its boundary. The remainder of its boundary is given by portions of the places x = 0, y = 0, and z = 0. Compute the triple integral of z over this region in space. (You should probably begin by sketching this region.) 2 Let R denote the portion of the unit ball { ( x,y,z ) : x 2 + y 2 + z 2 ≤ 1 } that lies inside the solid cone { ( x,y,z ) : z ≥ radicalbig x 2 + y 2 } . Compute the volume of R with triple integrals in both cylindrical and spherical coordinates. 3 Let R denote the portion of the unit ball { ( x,y,z ) : x 2 + y 2 + z 2 ≤ 1 } that lies inside the prism { ( x,y,z ) : x ≥ 0, y ≥ 0, and x + y ≤ 1 } . Set up a triple integral to compute the volume of R ....
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This note was uploaded on 12/10/2011 for the course MAC 2313 taught by Professor Keeran during the Fall '08 term at University of Florida.
 Fall '08
 Keeran
 Calculus

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