Use Stokes Theorem to evaluate •[F F-dr where F(z, y, z)=zi+si+z²+ y²)k and C is the boundary of the part of the paraboloid where 2-16-2²-² which lies above the xy-plane and C is oriented counterclockwise when viewed from above.

Q: Does there exist a surface x(u, v) such that E=G=1,F=0 and L=1,M=−1,N=0?

A: The objective of the question is to determine if there exists a surface x(u, v) that satisfies the…

Q: Determine the flux of F(x, y, z) = across the surface with an upward orientation. Let the surface…

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Q: 2. Verify Stokes's Theorem for F(x, y, z) = y i+ z j +x k and the plane x + y + z = 2 in the first…

A: Given, Fx,y,z=yi^+zj^+xk^x+y+z=2 So, curl F is calculating by, Curl F→=∇→×F→Curl…

Q: Jo F-dr where F(x, y, z) = xi+yj + 6(x² + y²)k and C is the boundary of the part of the paraboloid…

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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: 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: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: The distance of a point P(x,y,z) from the xy plane is d = |x| how do we show the work to prove this?

A: To show the distance of a point P(x, y, z) from the xy-plane is d = |x|, it can use the distance…

Q: Use Stokes Theorem to evaluate [F F. dr where F(x, y, z)=zi+yj+22² + y²)k and C is the boundary of…

A: Given,C is the boundary of the part of the paraboloid where which lies above the xy-plane and C is…

Q: 1 − v2), 0 ≤ u ≤ 2π, v ≥ 0.

A: The surface S is a portion of a paraboloid that opens downwards, truncated at its base. To see this,…

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: Q3] (A) Verify Stokes' theorem where Ã= (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z =…

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Q: yzi + ³j+rzk, and S is the part of the sphere Verify Stokes Theorem for fas F-dr, where F r² + y²…

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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: (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: Find all equilibrium solutions (of the form (t) = xo, a constant) of the second-order differential…

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Q: a) Find the curl V×Fif F = (y',2xy,yz)

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Exercise 5. Compute F F.NdS where F(x, y, z) surface of the plane x + 2y + z = 6 in the first…

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Q: This surface (dreamed up by Steiner while in Rome) looks smooth but is non-orientable, with the…

A: Given: The parametrization for the surface is given by σ(u,v)=x,y,z=sin2usinv,sin2ucosv,cos2usin2v…

Q: Verify Stokes' Theorum for F(x,y,z) = (y,-x,yz) if S is the paraboloid z = x2 + y2 with x2 + y2 = 1,…

A: Given  Fx,y,z=y,-x,yz Then, F→=yi^-xj^+yzk^