Use Stokes' theorem to evaluate • Sf₂ (V x (V x F). dS where F(x, y, z) = -3yzi + 3xzj +6(x² + y²)zk and S is the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 1, oriented upward.

Q: Q8: Verify Stokes's Theorem f(x) ds = ff. dr for f = yî+j+xk and the paraboloid for the the surface,…

A:

Q: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: Use Stokes' theorem to evaluate (V x F) - ds where F(x, y, z) = −6yzi + 6xzj + 11(x² + y²)zk and S…

A:

Q: F. dr where C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = xyi + 3zj + 5yk,…

A:

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: Verify Stokes' Theorem for F(x, y,z)= (y,-x, yz) and S is the paraboloid z = x² + y° , 0<zsl. Assume…

A: ∫F→.dr→=∫∫Scurl F.n dA.Here  Fx,y,z=y1-x1 yzS  is the parabloid  Z=x2+y2, 0≤Z≤1

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: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

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

A: Given, F(x,y,z)=xyi+5zj+6ykwhere c is the curve of intersection of the plane x+z=3 and the cylinder…

Q: (a) Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = x2yi + x³j + xyk and C is the curve of…

A: Given F→x,y,z=x2yi+13x3j+xykWhere C is the curve of intersection of the hyperbolic paraboloid…

Q: eff curl(F). ds. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of the paraboloid z = 9 - x² -…

A:

Q: Use Stokes' theorem to evaluate // V x 7.1 ds where 7 = (9y²z, 3xz, 6x²y²) and S is the paraboloid z…

A:

Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

A:

Q: Use Stokes' theorem to evaluate f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

A:

Q: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

A:

Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)