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Unformatted text preview: , , 0) , (0 , 1 , 0) , (0 , , 2) and let C be the closed curve that bounds it. This triangle lies in the plane 2 x + 2 y + z = 2. a. Let f ( x, y, z ) = z , compute Z S f ( x, y, z ) dS. b. Let F = z 2 k , compute Z C F · d r 1 5. (20 pts.) Let F =-y i + x j x 2 + y 2 a. Compute ∇ × F . b. Let C 1 be a closed curve that does not go around the z axis. Compute I C 1 F · T ds c. Let C 2 be a closed curve that goes around the z axis once in the counter-clockwise direction. Compute I C 2 F · T ds 6. (10 pts.) Suppose F , G are conservative vector ﬁelds deﬁned in all of 2 space. Show that F + G is conservative. 2...
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- Spring '07
- Vector Calculus, 2 K, 10 pts, 20 pts