Use the divergence theorem to evaluate F.dS, where F = and S is the surface bounded by x2+y²=4, z =0, z =5. O a. None of these O b. 20n Oc. 18п d. 12 24п е.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Q4. Verify the divergence theorem A · dS V·A dv %3D for each of the following cases: (a) A = xy'a, +…

A: Note: Since you have posted multiple independent questions. According to our policy we are only…

Q: |Use the Divergence Theorem to evaluate || F•ndS where F(x, y,z)=(x+cos z)i+(2y+sin z)j+(z+e*)k .n…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Please calculate the curl as well as the divergence of the following map: F:R' → R given by: F(x, Y,…

A: To find the curl and divergence of a given vector field, we use the definition of curl and…

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: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: Use the Divergence Theorem to evaluate F. dS where F = (2²a +y?. + tan (2), a?z – 1 2, and S is the…

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Q: Exâmple '7.21 Evaluate the surface integral / y?2² dS where o is the part of the cone x2 + y? that…

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Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: Use Stokes' Theorem to evaluate F. dr, where F (x, y, z) = zi + yj – xk and C is the boundary of the…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: Q19// If F = yi +j- xk , Evaluate , F dv where V is region bounded by the plane z-0 and the surface…

A: 19Given that:¯The vector field is F→=yi^+j^-xk^ and the region R is boundedby the plane z=0 and the…

Q: If F = 2y i - zj + x²k and S is the surface of the parabolic cylinder y²= &x in the first octant…

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Q: Let S: x2 + y? = 9,0szS7 be the surface of a closed cyllnder bounding a volume T.F=Ly², x², z²J. Use…

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Q: Let F=[x+y, y+z, x+z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Topic- vectors

Q: Apply the divergence Theorem,with the surface of F = 4xzỉ – y²j + yzk and S being the cube surface…

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: Evaluate the following surface integral. ∫∫S (1 + yz) dS; S is the plane x + y + z = 2 in the first…

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Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Verify the Divergence Theorem SI div F av F. dS S E for F(r,y,2) = z i+ yj+xk and where E is the…

A: Given that Fx,y,z=z i+ y j +x k and E is the solid ball x2+y2+z2≤16. First find the divergence of F.…

Q: Let F=[-x, y, z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Hi, since you have asked multiple questions, we will solve the only one question for you. If want…

Q: Use the divergence theorem to evaluate I = F.N dS, where F = (ry?, yz², zx² ), and N is the the unit…

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Q: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

A: We will find out the required value.

Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: 10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F = <y,-x, zZ %3D 工=?

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Q: Use the Divergence Theorem to evaluate the surface integral |a? – 3y + 62) ds, S. here S is the…

A: Given the surface integral ∬Sx2-3y+6zdS, where S is the sphere x2+y2+z2=9. The integrand is a scalar…

Q: Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) ·…

A: a) Given the field, F=2x+yzi-2yj+z2+xk The surface S is the sphere x2+y2+z2=4 with an outward…

Q: Use the Divergence Theorem to calculate the surface integral f Ss F- dS where F(x, y, z)=x²yi+ry²j+…

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Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Evaluate || F:ñ dS where S is the surface bounded by z = a - Vx² + y² and the xy-plane including the…

A: The vector field is F→=xπ, yπ, 3z-2π. The surface is bounded by z=a-x2+y2 and xy-plane. The function…

Q: If F=xi+yj, prove that JF.ñds equals [V.FdA, where R is the disk of radius C R "a" and centre at the…

A: Given Data: F =xi  +yjTo Prove:∫C F . n ds =∫R∇·F dA where R is the disk of radius ''a'' and centre…

Q: Q19// A scalar filed V = xyz exists over a surface S defined by x? + y? = 9 bounded by the plane…

A: Given scalar field, V=xyz This field exists over a surface S defined by x2+y2=9 bounded by the plane…

Q: Verify the formula F.ndS = div F dV G in the Divergence Theorem by evaluating the surface integral…

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Q: Use the Divergence Theorem to evaluate  F · dS,  where  F(x, y, z) = z2xi +  + ((1/3)y3 + cos z)j +…

A: Given data:

Q: Let S:x+z? = 16,0sys3 be the surface of a closed cylinder bounding a volume T.F=[z?, y, x²]. Use the…

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Q: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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Q: 6. Use the Divergence Thm to calaulate the surface integral F.n dS (a) S is the boundary of the cube…

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Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

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Q: Sketch the reglons enclosed by the glven curves. y = Vx, y= X= 16 y y 6 4 4 3 3 2 10 15 10 15 O-1…

A: Given : y = √x  y = 1/3 x  x = 16

Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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Q: Q3// Evaluate ſ. F dS where F = xi + yj + zk and S is the surface x? + y? = 9_in the first two…

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Q: Q2// A surface S is defined by x? + z = 9 and the bounded by the planes y = 0, y = 1,x = 0, z = 0 in…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.