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If Fis a continuous vector field on an oriented surface S with unit normal vector n, then F.dS = S Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the ty-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, F. dr = == S, curl F. ds Select one: True False Let D be the interior of the circle of radius 2 centered at (3,0). Then F(z,y) = 2r 22 + y2 i + 2y j is a conservative vector field on D. 2 + y2 Select one: O True O False F(1, y, z) = yi + 3j is a gradient field. Select one: True False If S is the boundary of a simple solid region E, then the flux of a constant vector field across S is zero. Select one: True O False If Fis a continuous vector field on an oriented surface S with unit normal vector n, then F.dS = S Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the ty-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, F. dr = == S, curl F. ds Select one: True False Let D be the interior of the circle of radius 2 centered at (3,0). Then F(z,y) = 2r 22 + y2 i + 2y j is a conservative vector field on D. 2 + y2 Select one: O True O False F(1, y, z) = yi + 3j is a gradient field. Select one: True False If S is the boundary of a simple solid region E, then the flux of a constant vector field across S is zero. Select one: True O False