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TakeHomeQuizSolutions - Math 3010 Bonus Quiz Nov 16 2012...

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Math 3010 Bonus Quiz Nov. 16, 2012 Student number: Name: Select the best answer to the following questions. For questions 1-3 let C be an oriented simple curve in R n and let v c : [ a, b ] R n be an orientation-preserving parametrization of C . Let f : R n R and v F : R n R n be continuous on C . 1. Which of the following is equal to the path integral i C f ds ? s i b a f ( v c ( t )) · v c ( t ) dt s i b a f ( v c ( t )) · v c ( t ) dt i b a f ( v c ( t )) || v c ( t ) || dt s i b a f ( v c ( t )) || v c ( t ) || dt 2. Which of the following is equal to the line integral i C v F · dvs ? i b a v F ( v c ( t )) · v c ( t ) dt s i b a v F ( v c ( t )) · v c ( t ) dt s i b a v F ( v c ( t )) || v c ( t ) || dt s i b a v F ( v c ( t )) || v c ( t ) || dt 3. If v F = v f on C , which of the following is always equal to i C v F · ? s v F ( v c ( b )) v F ( v c ( a )) s v F ( v c ( a )) v F ( v c ( b )) f ( v c ( b )) f ( v c ( a )) s f ( v c ( a )) f ( v c ( b )) For questions 4-6, let C be the straight segment in R 2 starting from point (0 , 1) and ending at point (1 , 2).
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TakeHomeQuizSolutions - Math 3010 Bonus Quiz Nov 16 2012...

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