MATH 251H Final Exam Version B Solutions

Compute the flux through c 1 2 2 1 5 f ds 2r 4 4 sin

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Unformatted text preview: l vector:  2r sin   k r cos 2  r sin 2   N  î 2r cos  *  This is up and in. Reverse N  2r cos , 2r sin , r  h. Evaluate F  2xy 2 , 2yx 2 , z x 2  y 2 on the cone: 2 3 3  F  2r cos  sin , 2r sin  cos 2 , 2r 3 2r cos , 2r sin , r R r , i. Compute the dot product:  F  N  4r 4 cos 2  sin 2   4r 4 sin 2  cos 2  2r 4  2r 4 4 sin 2  cos 2  1 j. Compute the flux through C: 1 2 2 1 5  ÞÞ F  dS  Þ Þ 2r 4 4 sin 2  cos 2  1 dr d  2 r Þ sin 2 2 5 00 0 0 C 2 2 1 cos 4 cos 2 2 d  2 Þ d   2Þ 50 50 2 k. Complete the parametrization of the disk D:  R r,   r cos , r sin , 2 1 5 sin 4 4 1 d 2  0 2 5 l. Compute the tangent vectors: r  cos , sin , 0 e   r sin , r cos , 0 e m. Com...
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