Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3, center at (2, 0, 0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0, 0, 0). Find the flux of curl(F) across S and then evaluate the circulation f F. dr. (Use symbolic notation and fractions where needed.) s curl(F) curl(F). dS = F. dr =

Q: Find div F and curl F if F(x, y, z) = x²i – 5j + yzk. div F= curl F=

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Q: 4. Find the flux of F across S if F = yi-xj+2zk and S is the hemisphere x² + y² + z² = 4, z ≥ 0,…

A: We have to find flux passing through sphere.

Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

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Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The given data is: Let S be the paraboloid y=x2+z2 Find a parametric representation for S and its…

Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

Q: fy the notation that shows the transformation of triangle SML onto triangle S'M'L' to show the…

A: Explanation and solutions is given below....

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: Use Stokes' Theorem to find the circulation of F = 4yi + 4zj+ 3xk around the triangle obtained by…

A: We have to find ∫CF→·dr→ using Stokes'sTheorem

Q: Determine the curl and divergence of F(XYZ) = xye* ^-x³yze²^ + + xy²e¹ k

A: To find- Determine the curl and divergence of Fx, y, z = xyex i^ - x3yzez j^ + xy2ey k^.

Q: Suppose F = (6y, -2z, 6x) and S is that portion of the plane x + 2y + 3z = 1 that is the first…

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Q: 18)Find curl F and div F if F(x,y,z) = exsiny i + esinz j + e²sinx k

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Q: Nedd help with d)

A: (d) To determine if the given mapping T is a linear transformation on the plane R^2

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A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Suppose F(x, y) = (x² + 6y, 2x − 2y²). Use Green's Theorem to calculate the circulation of around…

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Q: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

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Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

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Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

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Q: Let F (8xy, 3y, 8z). = The curl of F = (000). Is there a function f such that F = V f? ☐ (y/ (y/n)

A: Step 1: Step 2: Step 3: Step 4:

Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: Let P be the tangent plane to the surface z-2x2+y2 at the point Q=(1,1,3). Which of the following…

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Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

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Q: Let F(x, y, z) = (x², 2xy + e³², 3ye³z). Find div F(1,2,0) and curl F(0, 1, 1).

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Q: Let FMN be the transformation of the surface. Prove F*dg=d (F*g) gEA (N) = S(N). where

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Q: Given: Find (a) div F (b) curl F

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Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: Suppose F(x, y) = es sin(x)] and C is the counter-clockwise oriented rectangle with vertices (0, 0),…

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Q: Use Stokes' Theorem to find the circulation of F = 2yi + 3zj + 7xk around the triangle obtained by…

A: Here we have to solve the given problem using stokes' theorem.

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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