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Verifying Stokes’ Theorem Verify that the line
10. F = 〈–y –x, –z, y – x〉; S is the part of the plane z = 6 – y that lies in the cylinder x2 + y2 = 16 and C is the boundary of S.
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Chapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
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- Q2. Verify Stoke's theorem for the vector function, F = xî+ z² ĵ+ y² k over the plane surface x +y + z = 1 lying in the first octant (figure is necessary for the answer of Q2.)arrow_forwardStreamlines and equipotential lines Assume that on ℝ2, the vectorfield F = ⟨ƒ, g⟩ has a potential function φ such that ƒ = φxand g = φy, and it has a stream function ψ such that ƒ = ψy andg = -ψx. Show that the equipotential curves (level curves of φ)and the streamlines (level curves of ψ) are everywhere orthogonal.arrow_forwardUse Stokes' Theorem to evaluate Use Stokes' Theorem to evaluate ∫C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 3xzj + exyk, C is the circle x2 + y2 = 4, z = 6.arrow_forward
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- please indicate whether parallel perpendicular or neitherarrow_forwardTop The base of the closed cubelike surface shown here is the unit square in the xy-plane. The four sides lie in the planes x=0, x= 1, y = 0, and y = 1. The top is an arbitrary smooth surface whose identity is unknown. Let F=xi - 2yj + (z + 3)k and suppose the outward flux of F through Side A is 1 and through Side B is - 3. Can you conclude anything about the outward flux through the top? Give reasons for your answer. Side A Choose correct answer below, and, if necessary, fill in the answer box to complete your choice. A. Yes, the outward flux through the top can be calculated exactly, and it is (Type an integer or a fraction.) B. Yes, the outward flux through the top is positive, but it cannot be calculated exactly. C. Yes, the outward flux through the top is negative, but it cannot be calculated exactly. D. No, the outward flux through the top cannot be determined without its identity. Give reasons for your answer. O A. By the Divergence Theorem, the outward flux is 0. Side A and…arrow_forward2. A cartesian equation for the surface is? 3. Draw the grapharrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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