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13 Nov 2019
It turns out that F (the field from problem 6) Use this fact, Stokes' Theorem, and properties of surface/line integrals to answer problem 6 without y , z , zy-yH) satisfies â½ Ã F-(z-z? , 2ry , 2). doing any computations.
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Consider the vector field F(x,y,z) = xi + 3xzj + -2yk and the surface S which is the part of the plane x + 2y + z - 3 that lies in the first octant, oriented upward. Without making any calculations, is the flux through the surface positive or negative? Why? Calculate . What is the boundary dS of the surface? Set up and evaluate the line integral . Note that Stokes' Theorem applies. Which integral was easier to find?
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Verify Strokes Theorem is true for F=6yzi+2yj+xk on part of paraboloid z=2-x^2-y^2 and lies above the plane z=1 oriented upwards
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