m264508..-4

m264508..-4 - Nurul Hanim Hashim WeBWorK assignment 4 due...

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Unformatted text preview: Nurul Hanim Hashim WeBWorK assignment 4 due 5/27/08 at 11:59 PM. 4.(2 pts) Consider the vector field F x y z 6yz 7xz 4xy . Find the divergence and curl of F . div F ∇F . curl F ∇F , , . Correct Answers: 0 (4 - -7)*x (6 - 4)*y (-7 - 6)*z 5.(2 pts) Apply the Laplace operator to the function h x y z e 6x sin 2y . ∇2 h . Correct Answers: exp(-6 * x) * sin(2 * y) * (-6*-6 - 2*2) 6.(2 pts) Use Green’s theorem to compute the area of one petal of the 8-leafed rose defined by r 9 sin 4θ . It may be useful for recall that the area of a region D enclosed 1 by a curve C can be expressed as A x dy y dx. 2C Correct Answers: 15.9043128087983 ¥ ¨  ¢ § § § ¢ ¢¡ ¡ ¢ ¡ ¨ ©¡ §¢¡ ¡ §  §  §¢ ¢ § §¢ ¥ ¥ ¥ ¥ ¥  MATH264 May 2008 1.(2 pts) Let C be the positively oriented square with vertices 0 0 , 1 0 , 1 1 , 0 1 . Use Green’s Theorem to evaluate the line integral C 10y2 x dx 4x2y dy. Correct Answers: -3 § ¦ ¤ ¦ ¢ ¤ ¡ ¢ ¡ £ ¢ ¡ ¢ ¡ 2.(2 pts) Find a parametrization of the curve x2 and use it to compute the area of the interior. Correct Answers: 1.17809724509617 3.(2 pts) Let F 4yz i 8xz j 3xy k. Compute the following: A. div F B. curl F i j k C. div curl F Note: Your answers should be expressions of x, y and/or z; e.g. ”3xy” or ”z” or ”5” Correct Answers: 0 (3 - 8)*x (4 - 3)*y (8 - 4)*z 0 ¢ ¤ ¢ ¤ ¤ ¢ ¤ § § § § ¥ ¥ ¥ ¥ ¥ Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR  ¥ ¥ 3 y2 3 1 1 ...
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This note was uploaded on 01/10/2011 for the course MATH 264 taught by Professor Johnson during the Summer '10 term at McGill.

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