vctut05 - x + 3 y + 5 z = 15 where x 0, y 0 and z 0. 4....

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The University of Sydney School of Mathematics and Statistics Tutorial 5 MATH2061: Vector Calculus Summer School 2012 1. (a) Draw a sketch of the surface S deFned by: x = 2 cos θ sin φ, y = 2 sin θ sin φ, z = 2 cos φ, for θ : π/ 2 π/ 2 and φ : 0 π/ 2. (b) Evaluate ii S xe x 2 + y 2 + z 2 dS where S is the surface in part ( i ). 2. If F = y 2 i + y j + xyz k , evaluate ii S F · n dS where S is the curved surface of the cylinder x 2 + y 2 = 4 , 0 z 2 , and n is the unit outward normal. 3. ±ind the ²ux of F = i + j upwards through the triangular region of the plane
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Unformatted text preview: x + 3 y + 5 z = 15 where x 0, y 0 and z 0. 4. Evaluate the triple integral i 2 i x-1 i y (6 z + 1) dz dy dx. 5. ind the mass of the solid bounded by the surface z = 9 x 2 y 2 and the xy-plane, if the density of the solid at the point ( x, y, z ) is (1 + x 2 + y 2 ). Copyright c c 2012 The University of Sydney...
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