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Unformatted text preview: given by v = i + x j + z k in meters/second. How many cubic meters of uid 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 elds 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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This note was uploaded on 07/19/2010 for the course MA 1C taught by Professor Ramakrishnan during the Spring '08 term at Caltech.
 Spring '08
 Ramakrishnan
 Math, Calculus, Linear Algebra, Algebra

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