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 paraboloid x2 + y2 + z = 12 that lies above the plane z = 3 and is oriented upward. F. dS =

Q: 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…

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Q: Use a parameterization to find the flux F•n do of F = z°i+ xj – 4zk in the outward direction (normal…

A: We have to find the flux ∬SF·ndσ of F=z2i+xj-4zk in the outward direction across the surface cut…

Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the net flux through…

A: consider the equation

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (5x3…

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Q: F. dS; that is, calculate the flux of F across S. Js Use the Divergence Theorem to calculate the…

A: The divergence theorem states that:∬SF.dS =∫∫∫V div F dVwhere, S is the closed surface and V is the…

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i+ (y – x)j+ (z – y)k - across…

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Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: Use the Divergence Theorem to calculate the surface integral: SSF S F dS; that is, calculate the…

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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 a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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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: Let S be the cylinder x +y a, 0szsh, together with its top, x +y sa, z=h. Let F= -7yi + 7xj + 7x k.…

A: Given data: S is the cylinder, with its top x2+y2≤a and height0≤z≤h. Also Given a vector F→ Such…

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: Find the flux of F (x, y, z) = 4.xi+ 4yj+ 2k outward (away from the z-axis) through the surface cut…

A: The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ.…

Q: Let v = (4 xe cos y, y cos z, e cos y) be the velocity field of a fluid. Compute the flux of v - I…

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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…

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Q: Find the outward flux of F through S. F-Ñ dS where F(z, y, z) = -3zî+y³j+yk, and S is the surface of…

A: The general form of a vector valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: 3. Calculate the flux of the given field F across the given surface S. • F(r, y, z) 22 + y? = 4 and…

A: using divergence theorem

Q: Use the divergence theorem to compute the value of flux integral F. dS, where F(x, y, z) = 5yj - 5zk…

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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…

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Q: Use the Divergence Theorem to calculate the surface integral || F ds; that is, calculate the flux of…

A: F(x,y,z)=3xy2i+xezj+z3ky2+z2=9And the planes x=-3 and x=3

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 i = (a° cos z, 5 – 3a'y cos z – 3yz? sin æ, 2° sin æ) be the velocity field of a fluid. Compute…

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Q: Use the Divergence Theorem to calculate the flux [fF . d§, where F(x, y, z) = (1) (sin(yz) + yz)i +…

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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: Let v = (5, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=5,y sinz, cosz Flux=∫∫Sv⇀.ds we have divergence theorem, ∫∫Sv⇀.ds=∫∫∫Sdiv v⇀.dv div…

Q: Find the outward flux of F= (x')i+(y²)}+(z²)k across the boundary of the region D, where D is the…

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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: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x= 0, y=0,…

A: Given Vector field is F = 2xi + 3yj - zk

Q: Use the Divergence Theorem to calculate the outward flux of F = (r3 + y, y + z3, z3 + 23) across S:…

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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 E = {(x,y, z) | x² + y² < 1 and xy < z < 2} and let S be the boundary of E, oriented outward.…

A: Using Gauss divergence law:  ∯SF.dS=∫∫∫V∇·F.dV                   =∫∫∫V2+3-1.dxdydz…

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: Evaluate F-N dS and find the outward flux of F(z,y, z) = ryî+yzj-yzk, through %3D the surface S of…

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

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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…

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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…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2 i…

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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: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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Q: Let S be the cylinder x² + y² =a²2, 0≤zsh, together with its top, x² + y² sa², z = h. Let F = -7yi +…

A: Given : Surface S is the cylinder x2+y2=a2, 0≤z≤h, together with its top, x2+y2≤a2, z=h and  F→=-7y…

Q: : Let S is the part of the paraboloid z = 4-x2 - y? above the plane z = 1 oriented with upward…

A: We have to find the flux for the given surface.

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

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Q: Let F(x, y, z)= (sin (zy))i +(z° cosh x)j+(z² )k. Find the flux of F across the positively oriented…

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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: Consider the surface S given by y=8−x2−z2, y≥0 oriented in the positive direction of the y axis. be…

A: We will find out the required value.

Q: The region W lies between the spheres a? + y? + z2 = 9 and æ? + y² + z² = 16 and within the cone z =…

A: Here we can use divergence theorem to find the flux of the vector valued function. Divergence…

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…