Let F = < ²ez, ez, z²e¹y >. Use Stokes' Theorem to evaluate curlF rlFds, where S S is the hemisphere x² + y² + z² = 4, z ≥ 0, oriented upwards

Q: F= (y, 2x, -z) and C is the circle x² +y² = 9

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Q: > Let F =< x²e³², xez, z²exy :// curl F. dS, where S Use Stokes' Theorem to evaluate S is the…

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Q: Use Stokes' theorem to evaluate I = ff, Vx F. ds where F = (2²,-3xy, x³y³) and S is the part of z =…

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Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = 4y cos(z) i + e\ sin(z) j + xeY k, S is the…

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Q: Find VX A for the vector A given by A = -yax + x ay Evaluate Ad A de around the curve x² + y²2 = 1…

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Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

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Q: Let S be the downward-pointing cone whose base is the unit circle in the ry-plane centered at the…

A: Here given that unit normal vector is outward sence,that is if  be the unit normal vector to the…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = zei + x cos(y)j + xz sin(y)k, S is the…

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Q: Let = In 2r, where r = √² + y². Express V as a multiple of the unit radial vector ê, = ( ) in R2…

A: We are given functionwhere

Q: find the principal curvatures and principal vectors of the saddle surface M:z = xy at the origin.

A: To find the principal curvatures and principal vectors of the saddle surface M: z = xy at the…

Q: eff(V x F) · ds where M is the hemisphere a² + y² + z² = 4, x ≥ 0, with the normal in . M Use…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: Ic F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk,…

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Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four…

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Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…

A: The given surface is a cube, where the bottom face is not considered. The surface in question has 4…

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: Let F = ·[F Use Stokes' Theorem to evaluate F. dr, where C' is the curve of intersection of the…

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Q: Let F . Use Stokes' Theorem to evaluate Ncur curlFdS, where S is the hemisphere x² + y²+z² = 9, z>…

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