Verify the formula /F-n ds = div F dV in the Divergence Theorem by evaluating the surface integral and the triple integral. F(r, y, z) = 2ri – yzj + z°k where o is the paraboloid z = x² + y? capped by the disk x? + y < 4 in the plane z = 4.

Q: Find the surface area of the surface parametrized by φ(u, v) = (u2 + v, u, v) with 0 ≤ v ≤ 4 and…

A: The given surface is:ϕ(u, v)=u2+v, u, v

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

A: Given

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: Use Stokes' theorem to evaluate • Sf₂ (V x (V x F). dS where F(x, y, z) = -3yzi + 3xzj +6(x² + y²)zk…

A: Given vector field isF(x,y,z)= -3yzi+3xzj+6(x2+y2)zkAnd S is the part of paraboloid z = x2+y2  that…

Q: (1) Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the…

A: Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the double…

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: Evaluate the surface integral 1 d.S where o is the portion of the plane z = 4 - 6x – 1y in the first…

A: To find  where  is the portion of the plane  in the first octant

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: L₂F F = (4x³z, 4y³z, 3z¹) S is the surface of the solid bounded by the hemispheres 16 — x² - y², z =…

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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: Show that a group G of order par for district primes p and q is solvable

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Q: Let F = 2x3i + 2y3j + 2z3k and let S be the surface consisting of the hemisphere x2 + y2 + z2 = 1, z…

A: Given, F=2x3i+2y3j+2z3k and  S be the surface consisting of the hemisphere x2+y2+z2=1, z≥0 and the…

Q: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

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Q: The complement of a graph G is a new graph formed by removing all the edges of G and replacing them…

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Q: ​Money markets are markets for ​Foreign stocks. ​Consumer automobile loans. ​U.S. stocks.…

A: The objective of the question is to identify what money markets are markets for among the given…

Q: ify Stokes' theor d S is the surface

A: INTRODUCTION: Stoke's Theorem:-…

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: Evaluate f(3x1 + 2yj). ds where S is a sphere x² + y² + z² = 9

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Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Use Stokes' theorem frotF. ds to evaluate F(x, y, z) = (x + tan¯¹yz)i + y²zj + zk, S is the part of…

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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…