Let F(x, y, z) = z tan-(y²)i + z³ In(x² + 2)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 6 that lies above the plane z = 2 and is oriented upward. F. dS =

Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

Q: Let  F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 3)j + zk.  Find the flux of F across S, the part of the…

A: The flux of any vector field F→(x,y,z) across some closed surface S, such that the surface S bounds…

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region D. F = y…

A: The divergence theorem states:

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: Let F (x, y, z) = and G be the solid | Let below the paraboloid % = 4 – x* – Y° and above the…

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Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the…

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Q: Let S be the cylinder x +y = a°, 0szsh, together with its top, x² +y° sa, z=h. Let F= - 4yi + 4xj +…

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Q: 29. Let K be the part of the cone z = Vx2 + y? between z = 1 and z 3, oriented upward. Let F(x, y,…

A: Flux through the fluid

Q: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h>0z=0 Also F→=x2, y2, z2 To…

Q: 3. Consider the vector field F = (y, -x, x² + y?). Find the flux of F through S if: 9– x2 – y? above…

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Q: The outward flux of F(x, y, z) = xi + yj + zk across any unit cube is.

A: Given flux is F=xi+yj+zk. Compute div F. divF=∂∂xx+∂∂yy+∂∂zz=1+1+1=3

Q: Let F(x, y, z) = z tan-1(y?)i + z In(x2 + 8)j + zk. Find the flux of F across S, the part of the…

A:

Q: Find the net outward flux of F = a x r across any smoothclosed surface in ℝ3, where a is a constant…

A: Net outward flux is ∇.F ∇=i∂∂x+j∂∂y+k∂∂za=a1i+a2j+a3kr=xi+yj+zk

Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: Let v (2, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the surface…

A:

Q: Let F =. Find the flux F n ds, where C is the boundary, taken counterclockwise, of the rectangular…

A: Given function is F=xy, x2y                   (1) Since we know that, for function F=P, Q, the flux…

Q: Let F(x, y, z) = (x – ye?, y + xe?,8 – 2z) and G be the solid below the paraboloid z = 4 – x² – y?…

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Q: Use the Divergence Theorem to evaluate F.NO N ds and find the outward flux of F through the surface…

A: Note the following result :  Gauss divergence theorem : ∫∫SF⇀.N⇀dS =∫∫∫Ddiv(F⇀)dV ,where S is an…

Q: Let F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…

A: The given problem is to find the flux of vector field over the given surface of part of the…

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F across S, the part of the…

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Q: Let F(x, y, z) = z tan-1(y2)i + z³ In(x² + 6)j + zk. Find the flux of F across S, the part of the…

A: Using divergence theorem:  ∬SF.dS=∭VdivF.dV…

Q: Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find…

A:

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x*i+ 3x?yj+ 23xyk across the surface of…

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Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

Q: Let F(x, y, z) = z tan-(y?)i + z³ In(x? + 4)j + zk. Find the flux of F across S, the part of the…

A: The given vector field is. Fx,y,z=z tan-1y2i^+z3 lnx2+4j^ +zk^ Let S be the top of the paraboloid…

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 4)j + zk. Find the flux of F across S, the part of the…

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Q: Let F (x, y, z) = and G be the solid %3D | below the paraboloid % = 4 – x" – y° and above the…

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Q: Let E be the solid region bounded by the upper half-sphere x² + y? + z2 = 4 and the plane z = 0. Use…

A: Flux of a vector field F→ along surface S =∫∫SF→.dS Divergence theorem  ∫∫SF→.dS→=∫∫∫E divF→dV Where…

Q: Set up an iterated double integral for the flux integral S ſ, F•dS where F(x, y, z) = ri+ yj+2k and…

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Q: Let F(x, y, z) = z tan¬1(y²)i + z³ In(x² + 9)j + zk. Find the flux of F across S, the part of the…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Find the total flux of the field x+ /1+ y² + z² 2y + V1+x²+ z² \3z + /1+x² + y², F(x,y, z) = out of…

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Q: Find the flux of the vector field F(x,y,z) = xi – yj + zk across o, where o is the portion of the…

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Q: Given the radial field (x, y, z) (x² + y² + z²)³/2 |r|3/2 Find the outward flux across the sphere of…

A: Image is attached with detailed solution.

Q: Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 1)j + zk. Find the flux of F across S, the part of the…

A: Divergence Theorem states that  Where S is a closed surface, and E is the region inside that…

Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

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Q: Suppose F(x, y, z) = (x, y, 3z). Let W be the solid bounded by the paraboloid z = x2 + y? and the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the outward flux of the field F = xz i + yz j + k across the surface of the upper cap cut from…

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Q: 2. Let F = (sin(22)e² - y²)i + (x² - cos z)j + (x²e³²)k. Consider the tetrahedron, oriented with…

A:

Q: Let F(x, y, z) = z tan−1(y2) i + z3 ln(x2 + 8) j + z k. Find the flux of F across S, the part of the…

A:

Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: Let F(x, y, z) = z tan-(y2)i + z³ In(x2 + 9)j + zk. Find the flux of F across S, the part of the…

A: Get points of intersection of the paraboloid and z=3:  Thus, point of intersection is a circle in…

Q: 8. Use the Divergence Theorem to find the outward flux of F(r, y, 2) = (y² + 2) i+y²j+(e® + z) k…

A:

Q: Let F(x, y, z) = z tan-1(y²)i + z³ In(x² + 1)j + zk. Find the flux of F across S, the part of the…

A:

Q: Let S be the piece of the surface z = 9-r that lies inside the cylinder r2 +y² = 9, and let F = (x,…

A: Given, S be the piece of the surface z=9-x2 that lies inside the cylinder x2+y2=9, and let F=x,y2,z.…

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F across S, the part of the…

A: Given that    Fx,y,z=z tan-1y2i+z3Inx2+6j+2k Also, the part of paraboloid x2+y2+z=6 that lies above…