Q3mat237 - 1. [6 marks, 3 marks each part] Evaluate (a) C z...

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1. [6 marks, 3 marks each part] Evaluate (a) ds z C where C is parametrized by π 2 0 , ) , sin , (cos ) ( = t t t t t g . (b) , where C is the line segment from (1, 1, 1) to (1, 2, 3). dz x dy z dx y C + + 2
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2. [6 marks] Evaluate , where C is the triangle dy y x dx e xy C x ) cos ( ) arctan ( 4 2 + + with vertices (0, 0), (1, 0), and (1, 1) oriented clockwise. 3
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3. [6 marks] Find the flux of k j i F y z + = 2 across the “quarter” sphere in the upward direction } 0 , 0 , 4 : ) , , {( 2 2 2 = + + = z x z y x z y x S (that is evaluate ∫∫ where n points away from the center). S dS n F 4
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4. [6 marks] Let k j i r z y x z y x + + = ) , , ( and a = ( k , k , k ), where 0 k is a constant. Find the value (if any) of a constant m , such that the equality
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This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto.

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Q3mat237 - 1. [6 marks, 3 marks each part] Evaluate (a) C z...

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