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Unformatted text preview: 4. Find and classify the extrema of f ( x, y ) = xy2 xy . 5. Find the area of the part of the surface z = x 2 + y 2 that is cut o± by the plane z = 4. 6. Reverse the order of integration in the iterated integral Z 22 Z √ 4y 2 f ( x, y ) dx dy. 7. Calculate the work done by the force F ( x, y, z ) = ( yz + 1) i + ( xz + 1) j + ( xy + 1) k along the path consisting of line segments from (0 , , 0) to (2 , , 0) to (2 , 3 , 0) to (2 , 3 , 4). [ hint : Is F a conservative vector Feld?] 8. Calculate I C ( x 2 + 4 xy ) dx + (2 x 2 + 3 y ) dy around the ellipse C given by x = 4 cos t , y = 3 sin t , 0 ≤ t ≤ 2 π ....
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 Spring '08
 Gregorac
 Math, Calculus, Equations, Force, conservative vector field

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