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: 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: 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: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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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: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

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: Consider the surface S given by: S: r(u, v) = (uv, u² + v³, 3v²), u € [0, 2], v € [0, 1] whose…

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Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

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: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

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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: Evaluate each side of Stokes theorem for a portion of sphere : r=2m , Θ = π/3, 0 < ɸ < π H= 2r cosΘ…

A: This question is about application of stkoes theorem

Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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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: Find the divergence. and.cur.f the fallowin.. vecter field: a. È =xej+ ye k. %3D

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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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