Jse Stokes' Theorem to evaluate F. dr where F(x,y, z) = xi + yj+ 2(x² + y²)k and C is the boundary of the part of the paraboloid where

Q: X+ 3y and the planes Enclosed by the paraboloid z x= 0, y= 1, y = x, z = 0 13D

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

A: In this question, the concept of the tangent plane is applied. The equation of the tangent plane of…

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x² +y that lies above the…

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Q: Evaluate F.dr, where F (x, y, z) = - yi + xj + z*k and C is the curve of intersection of the plane y…

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Q: Q– Fin the surface area of the portion of the paraboloid z= 6-2x - y that is above the x-y plane…

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Let the surface xz – yz³ + yz? = 2, then - the equation of the tangent plane to the surface at the…

A: Equation of tangent plane of the surface f(x,y,z) =0 at (x0,y0,z0) fx (x0 ,y0 ,z0 )(x-x0) +fy (x0…

Q: 6. Use Stokes' Theorem to evaluate fF.dr, where F = xzi + xyj + 3xzk and C is the boundary of the…

A: The given problem is to evaluate the given line integral of the given vector field over the given…

Q: (3x – 2y +32) 7 + (4x – 2y +32) j +(2x – 6. Use the Stokes theorem to evaluate f FdT where F 3y |…

A: The given field is F→=3x-2y+3zi→+4x-2y+3zj→+2x-3y+2zk→. The boundary for the line integral is the…