Given F(x, y, z) = -xị + yzj + xyzk be a vector function that passes through a surface S of z+x² + y² = 9 that lies above z = 0, which is positively oriented. Sketch the surface S based on the given information, then evaluate ff.curl F n dS by using Stokes' Theorem. %3D

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Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Given:     Stokes'Theorem :                            ∫cF·dr =∬scurlF·ds   If F=Pi+Qj+Rk,…

Q: Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v) = [u, u³, v],…

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Q: Use Stokes' Theorem to evaluate F · dr where C is oriented counterclockwise as viewed from above.…

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Q: Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v)= [u, u, v],…

A: Step:-1 Given that Gx, y, z =1+9xy12  And   r u, v = u, u3, v0≤u≤1,  -1≤v≤1 So,  Gx, y, z =1+9xy12…

Q: Use Stokes' Theorem to evaluate fr F. dr. F(x, y, z) = xy i+ xºj + z² k where C' is the intersection…

A: To find- Use Stokes' Theorem to evaluate ∮CF·dr. Fx, y, z = xy i + x6 j + z2 k where C is the…

Q: Verify Stokes's Theorem for F = z²î+ x²j + y²k and S is the surface z2 = x2 + y², y 2 0, and 0 <…

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Q: Verify the formula fF-T ds = [ (curl F) -n ds in Stokes' Theorem by evaluating the line integral and…

A: According to the given information, it is required to verify the stokes theorem.

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: Consider the provided question,

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

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

A: Please see the explanation below

Q: 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SSV × F·n dA…

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Q: Let F = yz, xz, xy > . // curlF dS, where Use Stokes' Theorem to evaluate - x² – y? that lies above…

A: Given that F=-yz,xz,xy The paraboloid is z=8-x2-y2 and z=7 Finding the plane of intersection,…

Q: Evaluate Curlv•ñ , where v = 2xyi + (x² – 2 y)] + xzk and ñ is a unit vector normal to the surface…

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Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Given the vector field F = (z, x, y), calculate the flux of the curl of F through the portion of the…

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Q: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

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Q: Evaluate Curlv.ñ , where v = 2xyi +(x² – 2y)j + xzk and ñ is a unit vector normal to the surface…

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Q: implement Stokes ' Theorem by taking the vector function Å = (x² + z)i + (y² + x)j+ (z² + y)k on the…

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Q: Verify Stokes' theorem for the vector ficld v=x'i+x' yj. C is the boundary of the rectangle whose…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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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: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: Use Stokes theorem to evaluate V × F · dS over the surface of the paraboloid z = 5 – x² – y? above…

A: Given, F=y-3zi+x2-4zj+x+3yk The surface S is the region bounded by the paraboloid z=5-x2-y2 above…

Q: (ii) Use Stokes' Theorem to evaluate SF · dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function is F(x,y,z)=x2z i^+xy2 j^ +z2k^ . Plane: x+y+z=1 Cylinder: x2+y2=9 The objective is…

Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the…

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And,…

Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Verify Stokes' Theorem if F(x, y, z) = (x – y)i + (y – z)j+ (z – x)k and S be the portion of the…

A: Solution: The objective is to verify the Stokes theorem for the given problem

Q: Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v)= [u, u', v],…

A: According to the company policy, we are supposed to answer the first question only. For the rest…

Q: Given F(x, y, z) = -yzi + xzj - xyzk be a vector function that passes through a surface S of z +x? +…

A: Given, Fx,y,z=-yzi+xzj-xyzk be a vector function that passes through a surface S of z+x2+y2=20 that…

Q: Let G(x, y, z)= (1+9xy)? and consider a surface S given by the parametrization rlu, v)=[u, u", v],…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given:

Q: 4. Let S is the surface z = 5- - y, 1s z in R. Let S be oriented with the normal vector pointing…

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Q: Verify the formula fr F.T ds = = ff. (cur (curl F). n dS in Stokes' Theorem by evaluating the line…

A: Stokes theorem is verified

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

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Q: c) Use Stokes' theorem to evaluate + (zy – y) i – In z j+ (r + x*) k) · dr, where C is the…

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Q: Use Stokes' theorem to evaluate curl(F) · ds. F(x, y, z) = exYi + ej + xzk, Sis the half of the…

A: Given: F(x,y,z)=e4xy i+exz j+x2z k The half of ellipsoid 8x2+y2+8z2=8 To find:  ∫S∫curl(F). dS Use…

Q: iv) Given F (x, y, z) = -yzį + 2xj + xyzk be a vector function that passes through a surface S of z+…

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Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

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Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top…

A: The given problem is to evaluate the surface integral using stokes theorem where S is the surface of…