c3-t4 - Name TEST4/MAC2313 Page 1 of 6 Read Me First Show...

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Name: TEST4/MAC2313 Page 1 of 6 ______________________________________________________________________ Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations. Write using complete sentences. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Generic vector objects must be denoted by using arrows. Since the answer really consists of all the magic transformations, do not "box" your final results. Show me all the magic on the page neatly. ______________________________________________________________________ 1. (10 pts.) Let F ( x , y , z ) = < x 2 , -2, yz >. Compute the divergence and the curl of the vector field F . (a) div F = (b) curl F = ______________________________________________________________________ 2. (10 pts.) Convert the given iterated integral into an iterated integral in polar coordinates that has the same numerical value and is easier to evaluate, perhaps. Do not attempt to evaluate the iterated integrals. A picture might help. 0 3 (9 x 2 ) 1/2 0 2 x ( x 2 y 2 ) dydx
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TEST4/MAC2313 Page 2 of 6 ______________________________________________________________________ 3. (10 pts.) Write down the triple iterated integral in cylindrical coordinates that would be used to compute the volume of the solid G whose
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