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Unformatted text preview: of decrease of f at P (2 ,-1 , 2) and the direction in which this rate of decrease occurs. (b) Find all points on the ellipsoid 2 x 2 + 3 y 2 + 4 z 2 = 9 at which the tan-gent plane is parallel to the plane x-2 y + 3 z = 5. (6) (a) Let σ denote the boundary of the solid bounded by the paraboloids z = x 2 + y 2 and z = 18-x 2-y 2 . Find the surface integral RR σ F · n dS , where F = x i-y j + z k and the surface σ is oriented outward. (b) Calculate the surface integral RR σ F · n dS , where σ is the upper half hemisphere x 2 + y 2 + z 2 = 4, z ≥ 0 oriented upward and F = x 4 yz 4 i-2 x 3 y 2 z 4 j-x 2 k . 1...
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This note was uploaded on 09/30/2010 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.
- Fall '09