Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F=xi+xyj + yk; C: the counterclockwise path around the perimeter of the rectangle in the xy-plane formed from the x-axis, the y-axis, x=1 and y=7 49 DA. 2 B. 49 C. -49 49 D. 2

Q: 2. Let vector field F=(xz,-y,z) and surface, S is a cylinder x+y = 4 for 3<z<0 with %3D outward…

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Q: Determine the vector field of F Flr, y) = yl – x)

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Q: Calculate the circulation, SoF. dr. in two ways, directly and using Stokes' Theorem. The vector…

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Q: of the following equations would produce the direction field above

A: Given the graph is                 .

Q: (d) Compute curl F.

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Q: Use Green's Theorem to find the work done by the force field F(x, y) = Vyi+ Vxj on a particle that…

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Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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Q: ind the work done by force F = zi + xj + yk in moving an object over the curve r(t) = sin ti+ costj+…

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Q: Use Stokes' Theorem to calculate the circulation of the field F around the curv F=xi+xyj+yk; C: the…

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Q: dy Sketch the direction field for dx y II

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Q: Determine the vector field of F Flr, y) = yl – x)

A: Solution is given below:

Q: ) Verify Stokes' Theorem for the hemisphere S : x²+y²+z² = 9, z > 0, %3D its bounding circle C: 1?…

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Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

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Q: Use Green's Theorem to find the work done by the force field F(x, y) = Vgi + Væj on a particle that…

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Q: Which equation matches the direction field below? O dy da de dz =2x-y V-25 = sin a siny 11 || 2x V

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Q: Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Sketch a directional field for the equation. Identify at least 4 isoclines. dy dx = y +x Isoclines:

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Q: Consider the triangle shown in the figure below. a. Find the equation of the straight edge OA. b.…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 8x i + 8y…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = xi +yj+ z 2…

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