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Unformatted text preview: , , 0) , (0 , a, 0) and (0 , , a ), taken in that order. Extra questions for outside the tutorial 5. (From the MATH2001 exam, 2000.) Let S be the surface consisting of the hemisphere S 1 de²ned by z = r a 2 − x 2 − y 2 , and the disc S 2 given by x 2 + y 2 ≤ a 2 , z = 0. (a) Find the ±ux of the vector ²eld F = ( ye z + x 3 ) i + ( x 4 sin z + y 3 ) j + z 3 k outwards through the whole surface S . (b) Find also the ±ux of F upwards through the top hemisphere S 1 . (c) Now instead let F be de²ned by the formula F = ∇ × (4 yz 2 i + 3 x j + xz k ) . Calculate the ±ux of F upwards through the hemispherical surface S 1 . Copyright c c 2012 The University of Sydney...
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.
 Three '09
 NOTSURE
 Statistics, Vector Calculus

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