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# mter2 - Math 32B Winter 06 Midterm 2 Name 1 2 3 4 5 6 total...

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Math 32B, Winter 06, Midterm 2 May 12, 2010 Name: 1 2 3 4 5 6 total There are six problems. You have 50 minutes. Do as many problems as you can in this time, skip those which you cannot solve. Each problem is worth 5 points. You are not allowed to use calculators . .......... Good luck! 1

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Problem 1 Answer “yes” or “no” to each of the following five questions: 1. Is curl( f ) = 0 for all functions f : IR 2 IR? ............... 2. Is every conservative vectorfield F : IR 2 \ { (0 , 0) } → IR 2 irrotational? ............... 3. Do we have div ( f ) = 0 for every function f : IR 2 IR? ............... 4. Is the following statement correct? “A vectorfield F : D IR 2 on some domain D IR 2 is conservative if and only if every line integral of F over a closed curve C in D is equal to 0.” ............... 5. Is the following statement correct? “Given some parameterized curve and some vector field, the line integral of F along this curve depends only on the path described by the parameterized curve, but not on the specific parameterization.” ...............
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