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Unformatted text preview: ) = h z,x,y i . Compute the line integral R C F .d r (for whichever orientation you like). 5. Let F ( x,y,z ) = h xz,yz,xy i . Let S be the part of the sphere x 2 + y 2 + z 2 = 4 that is inside the cylinder x 2 + y 2 = 1 and above the xyplane. Compute ZZ S Curl F .d S . 1 2 Formulae These are included only to jog your memory  you are supposed to know what they mean. (a) SA = ZZ R s 1 + ± ∂f ∂x ² 2 + ± ∂f ∂y ² 2 dA. (b) Z C F .d r = Z C P dx + Q dy = ZZ R ∂Q ∂x∂P ∂y dA. (c) ∇ f = ± ∂f ∂x , ∂f ∂y , ∂f ∂z ² . Div F = ∂M ∂x + ∂N ∂y + ∂P ∂z . Curl F = ³ ³ ³ ³ ³ ³ i j k ∂ ∂x ∂ ∂y ∂ ∂z M N P ³ ³ ³ ³ ³ ³ . (d) ZZ S Curl F .d S = Z C F .d r ....
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 Spring '08
 Keeran
 Calculus, Geometry, Derivative, Vector Calculus, sphere x2, cylinder x2, Let, circle x2

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