Fall 2009 Final - MATH 1920, FALL 2009 FINAL EXAM SHOW ALL...

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MATH 1920, FALL 2009 FINAL EXAM SHOW ALL WORK. NO CALCULATORS. NAME: STUDENT ID #: SECTION #: Who is your TA? PROBLEM SCORE 1a 2a 3a 4a 5a 6a 7a 8 PROBLEM SCORE 1b 2b 3b 4b 5b 6b 7b 9 TOTAL:
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1. (a) (6 points) For what value(s) of c is the field F = ( y + cz ) i + x j + k conservative? Mark the correct statement below. You do not need to justify your answer. c = 0 . c = 1 . for every value of c. for no value of c . (b) (13 points) The field F = z cos( x ) i + e y ln( z ) j + ( e y z + sin( x ) ) k is conservative. Find a potential function for F . 1
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2. (a) (6 points) Consider the field F = x 2 i + y 3 j - xyz k . Mark the correct statement below. You do not need to justify your answer. div F = 2 x i + 3 y 2 j - xy k . div F = - xz i + yz j . div F = 2 x + 3 y 2 - xy . div F = 0. (b) (12 points) Let D be the region bounded below by the cone z = x 2 + y 2 and above by the sphere x 2 + y 2 + z 2 = 4. Compute the outward flux of F = x 3 z i + y 3 z j + 3 4 z 4 k across the boundary of the region D . 2
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3. (a) (6 points) The point (1 , 1 , 4) lies on the surface z = x 2 + 2 xy + y 3 . Mark the correct statement below. You do not need to justify your answer. 4
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Fall 2009 Final - MATH 1920, FALL 2009 FINAL EXAM SHOW ALL...

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