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Review 3

# Review 3 - y 2 z 2 = 4 and x 2 y 2 z 2 = 9 where the...

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MA 242 REVIEW 3 Find the mass of the plate bounded by y = (4 - x 2 ) 1 / 2 , y = x and the x-axis where the density is the distance to the x-axis. II. Find the mass of the plate bounded by x=y and x = y 2 where the density is the distance to the x-axis. III. Find the volume of the region bounded by 4 - y = x 2 , y = z and z=0. IV. Find the volume of the region bounded by z = ( x 2 + y 2 ) 1 / 2 and 6 - z = ( x 2 + y 2 ) 1 / 2 . V. Find the mass of the region that is between
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Unformatted text preview: y 2 + z 2 = 4 and x 2 + y 2 + z 2 = 9 where the density is the distance to the center of the spheres. VI. Find the mass of the region that is in the ﬁrst octant and also has bounds x 2 + z 2 = 1 and y 2 + z 2 = 1 and the density is the distance to the xy plane. (You can do this with Cartesian coordinates. Which direction do you want to go in ﬁrst?) 1...
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