251-f06-final

# 251-f06-final - MATH 251.504 Final Examination Name ID The...

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MATH 251.504 Final Examination December 11, 2006 Name: ID#: The exam consists of 9 questions. The point value for a question is written next to the question number. There is a total of 100 points. 1. [16] For each the following statements, indicate whether it is true or false . (a) Consider the vector ﬁeld F ( x, y, z ) = x i + y j + z k . Then div F = 3. Answer: (b) Let C be a smooth curve in R 2 with a certain orientation and let - C be the same curve with the opposite orientation. Then R C x 2 dx + y 2 dy = - R - C x 2 dx + y 2 dy . Answer: (c) Consider the vector ﬁeld F ( x, y, z ) = x 3 i - 7 xz j + 4 z k . Then RR S F · d S 0 for every sphere S in R 3 . Answer: 1

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(d) The vector ﬁeld F ( x, y, z ) = e y 2 z i + xyz j +( y 4 + xz 2 ) k is the curl of another vector ﬁeld. Answer: (e) The vector ﬁeld F ( x, y, z ) = x 2 y i + x 5 z 2 j + yz k is conservative. Answer: (f) The area of the disk { ( x, y ) : x 2 + y 2 1 } is equal to 1 2 R C x dy - y dx where C is the circle x 2
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## This note was uploaded on 07/22/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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251-f06-final - MATH 251.504 Final Examination Name ID The...

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