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Unformatted text preview: given by v = i + x j + z k in meters/second. How many cubic meters of ﬂuid per second are crossing the surface x 2 + y 2 + z 2 = 1 ,z ≥ 0? (Distances are in meters.) 7. (15 Points) Section 7.6, Exercise 18 . If S is the upper hemisphere { ( x,y,z )  x 2 + y 2 + z 2 = 1 ,z ≥ } oriented by the normal pointing out of the sphere, compute ZZ S F · d S for parts (a) and (b) . 2 (a) F ( x,y,z ) = x i + y j (b) F ( x,y,z ) = y i + x j (c) for each of the vector ﬁelds above, compute ZZ S ( ∇ × F ) · d S and Z C F · d S , where C is the unit circle in the xy plane traversed in the counterclockwise direction (as viewed from the positive z axis). (Notice that C is the boundary of S . The phenomenon illustrated here will be studied more thoroughly in the next chapter, using Stokes’ theorem.)...
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 Spring '08
 Ramakrishnan
 Math, Calculus, Linear Algebra, Algebra, Elementary mathematics, Standard basis, Versor

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