Use Stokes' theorem to calculate (V × A) · ndS with A = 3yi – xzj+ yz²k, where S is the surface of the paraboloid 2z = x² + y? bounded by z = 2 and C as the boundary.

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: 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: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: x² + y? that is below the plane Find the surface area of that portion of the paraboloid z = z = 2.

A: Given paraboloid z=x2+y2 Surface area, AS=∫∫R∂z∂x2+∂z∂y2+1dA AS=∫∫R2x2+2y2+1dA…

Q: The equation of the tangent plane to the surface 32 = x² + y² +1 at (-1,1,2) is O A.-2x-2y+3z = 2 O…

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Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

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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: c) Use Stokes' theorem to evaluate where F(x, y, z) = (x²+y²z) i+(x²+xy²) j+(x²+z²) k, and C is…

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Q: What is the surface area of a hyperbolic paraboloid described by parametric eqn: z = xy, where x,…

A: The surface area of a hyperbolic paraboloid described by the parametric equation z = xy, where x = u…

Q: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

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Q: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: Let Q be the rectangle formed by (0, 0, 0), (1, 0, 0), (0, 1, 1) and (1, 1, 1) oriented CCW as x² dx…

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Q: • SS,F. F = (4x³z, 4y³z, 3z¹) Calculate F.ds where and S is the surface of the solid bounded by the…

A: Given,                           F→=4x3z, 4y3z, 3z4, and S is the surface of the solid bounded by…

Q: Use Stokes' theorem to evaluate where = 3x²1+8x³yj + 3x²yk (V x F) - dA and S is the portion of the…

A: Given that S is the portion of the  plane that lies inside the box defined by the .

Q: The tangent plane and the normal line of the surface x = y? + z2 + l at (3, 1, -1) have the…

A: Solve the following