HW12Sol.pdf - Homework#12 Solutions Math 23 Spring 2015 1...

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Homework #12 Solutions Math 23, Spring 2015 1. Let S be the part of the plane containing the points (1 , 0 , 0) , (0 , 1 , 0) , and (0 , 0 , 1) that lies in the first octant (that is, with x 0 , y 0 , and z 0 ), with upward-pointing normal. (a) Let f ( x, y, z ) = x 2 + z . Compute RR S f dS .
(b) Let ~ F ( x, y, z ) = z ~ | - 2 x ~ k . Compute RR S ~ F · d ~ S .
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2. Find the surface area of the part of the sphere x 2 + y 2 + z 2 = 4 which is between the planes z = 1 and z = - 1 .

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