c3-t4

# In the first octant do not attempt to evaluate the

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in the first octant . Do not attempt to evaluate the interated integrals. G 1 dV ______________________________________________________________________ 6. (10 pts.) Compute the surface area of the portion of the hemisphere defined by z = (16 - x 2 - y 2 ) 1/2 that lies between the planes defined by z = 1 and z = 2.

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TEST4/MAC2313 Page 4 of 6 ______________________________________________________________________ 7. (10 pts.) Compute the work in moving a particle along of the path in the xy-plane that goes from the point (-1,-1) to the point (1,1) along the curve y = x 5 against the force field defined by F ( x , y ) y x , yx 3 . W ______________________________________________________________________ 8. (10 pts.) Starting at the point (0,0), a particle goes along the y-axis until it reaches the point (0,4). It then goes from (0,4) to (-4,0) along the circle with equation x 2 + y 2 = 16. Finally the particle returns to the origin by travelling along the x-axis. Use Green’s Theorem to compute the work done on the particle by the force field defined by F ( x , y ) = < -5 y 3 , 5 x 3 > for ( x , y ) ε 2 . [Draw a picture. This is easy??]
TEST4/MAC2313 Page 5 of 6 ______________________________________________________________________ 9. (10 pts.) (a) Show that the vector field

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in the first octant Do not attempt to evaluate the...

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