Find the mass of the lamina that is the portion of the cone z = x² + y² between z = 1 and z = 4 if the density is 8(x, y, z) = x²z. Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z = 3 – x² − y² in above the plane z = −1 with upward orientation.

Q: a) Compute the surface area of the portion of the plane x+y=z = 0 contained inside the cylinder x² +…

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Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

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Q: 2²2 F = 3xi + 3yj + zk and o is the portion of the cone z = √x² + y² between the planes z = 2 and z…

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Q: Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation…

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Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…

A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Find the flux of the vector field F(x, y, z) = [xy, yz, zx] through the cylinder x2+y2 <= 1, 0 <= z…

A: The given problem is to find the flux of the vector field through the given surface of the cylinder…

Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

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Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

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Q: Suppose C is a constant vector. Let F(x, y, z) = C find the flux of F through a surface S on plane…

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Q: 3. Let T: V→ V be a linear operator on a finite-dimensional F-vector space V. Let A₁,...,Ak E F be…

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Q: Find the flux of the field F(x,y,z)=z¹ i+xj- 6z k outward through the surface cut from the parabolic…

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Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

Q: Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane…

A: We have to find the flux F(x,y,z)=2xi+2yj+zk across the point of the paraboloid z=4-x2-y2 above the…

Q: Find the vector field flow F(x,y,z)=(x2,y2,z2)  through S, where S is a flat surface x+y=2, bounded…

A: The Divergence theorem, Let S be a piecewise, smooth closed surface that encloses solid E in space.…

Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

Q: Find the flux of F across S, 1.1. S F. N dS where N is the upward unit normal vector to S. F(x, y,…

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Q: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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Q: (b) Compute the flux of the vector field F(x, y, z) = yi + zk upwards through portion of the cone z…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x,y,z)=−3xy−2yzj+4xzk…

A: Given: And the radius of sphere S is 3.To Do: Calculate the Flux using the divergence theorem.

Q: a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius…

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Q: A quadrivector AH has components (1, 1, 1, 0, 1)' in the system S. Calculate the T components of AH…

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Q: Consider the surface S consisting of the portion the graph of the function z = x2 + y² above the…

A: (A) Given the surface S is z=x2+y2,  64≤x2+y2≤81. In cylindrical coordinates x=rcosθ,y=rsinθ, z=z,…

Q: e part of the plane with vector equation r(u, v) = (4 + v, u – 3v

A: Here we have to find the area of the part of the plane with vector equation r(u,v)=4+v, u-3v,5-4u+v…

Q: Let divF(x, y, z) 4x3 + 4y3 + 4z³ , where F represents the flow of a vector field. Estimate the flux…

A: Given that a small sphere of radius 0.1, centered at the point  (1, 1, 1).And                  div F…