Review 4 - IV. Find the work done by force F ( x, y, z ) =...

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MA 242 REVIEW 4 I. Find the mass of the surface 4 - z = ( x 2 + y 2 ) 1 / 2 above z=0 where the density is the distance to the z-axis. II. Find the flux through the part of the surface y + z = 2 that is inside y = x 2 and above z=0 of a fluid with velocity F ( x, y, z ) = < z, z, z > The orientation is up. . III. Find the flux of the fluid with velocity F ( x, y, z ) = < y, x, e z > through the part of surface x 2 + y 2 = 4 that is above z=0 and below y+z=2. The orientation is out of the cylinder.
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Unformatted text preview: IV. Find the work done by force F ( x, y, z ) = &lt; y, z, x &gt; along the path R ( t ) = &lt; t, t 2 , t &gt; from (0,0,0) to (2,4,2) V. Find the work done going counterclocwise around the closed curve that is a triangle bounded by x=0, x=y and y=2 through force F ( x, y ) = &lt; xy, e y 2 &gt; VI. Find C y 2 dx + (2 xy + z + 1) dy + ( y + 2 z ) dz from (1,1,1) to (3,2,1). 1...
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