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  3. 5 let s be the sphere 2 y221 and f...

Question: 5 let s be the sphere 2 y221 and f...

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5. Let S be the sphere 2 +y2+21 and F is some general differentiable curl F dA-0 in 3 vector field. Below you should explain why different ways: (a) Apply Stokes Theorem directly to J Js curl F dA; noting that (b) Write S = S+US where S+, S-are the upper/lower half spheres. the boundary of S is empty (why?). Note that both S+ and S have the same boundary C. Apply Stokes Theorem to J Jcurl F dA and J Js- curl F dA sep- arately. You should get the same integrals J F dT but with opposite signs. Explain why this happens (c) Compute and show that div(curl F)-0. Then apply the diver- gence theorem

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