Use Stokes' Theorem (in reverse) to evaluate (curl F) •nds where 1.2 F = : 5yzi + 6xj +5yzex²k,S is the portion of the paraboloid z = 11/2 normal on S points away from the z-axis. + y² for 0 ≤ z ≤ 2, and the unit

Q: Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of…

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Q: Find the equation of tangent plane to this surface at the point where x :1 and y = -1.

A: Given surface is z=f(x,y)=sin(π (3x+2y)) +x2y2 Equation of tangent plane is given by,…

Q: Verify Stokes' theorem where A = (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z=2-√√x² + y²…

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Q: Use Stokes' theorem to evaluate 0 F. dr. F(x, y, z) = zexi + (z − 7y³)j + (x − 5z³)k, C is the…

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Q: Evaluate SF. ds where F = (3xy², 3x M M is the surface of the sphere of radius 3 c the origin.

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Q: Let F=. SS S is the part of the paraboloid z = 13 - x² - y² that lies above the plane z = -3,…

A: Given That : The vector field F→=-yzi^+xzj^+xyk^ S is the part of the paraboloid z=13-x2-y2 that…

Q: Use Stokes's theorem to evaluate fF.dR or ff(V x F) ndo, whichever appears easier: F = xyi-yzj +…

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Q: Let F=. •[ f, cu S is the part of the paraboloid z = 10 - x² - y² that lies above the plane z = 9,…

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Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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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: Which of the centroid(s) are trivial

A: Note that : A region if is symmetric about y-axis then x-coordinate of the centroid of the region is…

Q: Let F = . Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (7,0,0),…

A: Given that, F→=5x+y2, 2y+z2, 8z+x2 And vertices of the triangle are, 7,0,0, 0,7,0, 0,0,7. To find…

Q: circle centered d complex varia tour integral egration is take

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Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

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Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = 2²i + 26xj – y°k | where C is the circle x2 + y²…

A: The objective is to find ∮CF.dr using Stoke's Theorem. Where F(x,y,z)=z2i+26xj-y3k and C is the…

Q: Find a parametric representation for the surface S, where S is the part of the cylinder x2+y2 = 4…

A: A surface S where S is the part of cylinder x2+y2=4 which lies between z=-2 and y+z=2. To Find:…

Q: ff curl(x²yi - rzk). n do over the closed surface of the ellipsoid 4 16 Warning: Stokes' theorem…

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Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: [[F F = (4r³z, 4y³z, 3z¹) S is the surface of the solid bounded by the hemispheres z = √9x² - y², z…

A: Since you have posted a multiple questions according to guidelines I will answer first question for…

Q: F(x, y, z) = yzi + 8xzj + exyk, C is the circle x² + y² = 1, z = 4.

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

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Q: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…

Q: prove hat for 4 x² + y² + z² + 6xyz + 2x² - y² +z²+ 4yz + 3zx = 0, rigin is a conic node. the locus…

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