SampleFinal

SampleFinal - Math2E, Lecture B Name: Signature: Sample...

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Math2E, Lecture B Sample Final Exam SQ08 Name: Signature: 1) Find and sketch the gradient vector field for , make sure the directions and magnitudes of the vectors are correct. 2 2 ) , ( y x y x f + = 2) Show that the vector field ) , ( ) , ( y y xe e y x F = K is conservative and find a scalar potential function for . Then evaluate the line integral f ) , ( y x F K C r d F K K where C is the part of the parabola connecting (0,0) to (1,1) . 2 x y = 3) Show that the vector field ) 1 , tan , tan 1 ( ) , , ( 2 1 1 2 z x x z x y z y x F + + + = K is conservative and then evaluate the line integral C r d F K K where C is the intersection of the hemisphere and the cylinder , in counterclockwise direction. 0 , 4 2 2 2 = + + z z y x 1 2 2 = + y x 1
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Math2E, Lecture B Final Exam SQ08 2 4) The vector field is given in the figure, determine if ) , ( y x F K C r d F K K is positive, negative or zero, where C is the upper half circle connecting (-1,0) to (1,0). Give reasons.
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This note was uploaded on 07/15/2008 for the course MATH 2E taught by Professor Wong during the Spring '08 term at UC Irvine.

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SampleFinal - Math2E, Lecture B Name: Signature: Sample...

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