Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4  and the elliptical cylinder 4x2 + y2 = 16.

Q: Let S be the closed cylinder bounded by the surface r2 + 2² = 4, and the planes y = 1 and y = 4. Use…

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Q: Use Divergence Theorem to evaluate || F·Nds and find the outward flux of F(x, y, z)=xi+yj+zkthrough…

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Q: Use divergence theorem to find the flux of F(x, y, z)=x²yî - xy²)+(2+2); o is the surface of the…

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

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: sing the Divergence Theorem, find the outward flux of F = 2xy 21 + 2x 2yj+ 5xy k across the boundary…

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Q: Evaluate both sides of divergence theorem for A = pa,+pcos(@)a , + za , through the closed surface…

A: Given vector field is  Divergence theorem

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x² + y)i+z°j+ (e° – z)k across the…

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Q: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: | Use Gauss Divergence theorem to calculate (5zi+ 4yj - 2: k).n dA over the sphere +y+ 9.

A: Here, let F=5x,4y,-2z⇒div F=∂(5x)∂x+∂(4y)∂y+∂(-2z)∂z=5+4-2=7

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i -…

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Q: Use the Divergence Theorem to calculate the flux of Flacross SI where F = zi + yj + zxk|and Slis the…

A: Given that F=zi+yj+zxk And, The objective is to find the .

Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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Q: use the divergence theorem to compute: F(x,y,z)=x2i+y2j+z2k; for the boundary of the solid region…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i + (y – x)j+ (z – y)k %3D -…

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Q: Let S be the closed cylinder bounded by the surface x2 + z2 = 4, and the planes y =1 and y = 4. Use…

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Q: Find |[F•N dS (flux), where F(x, y,z)= 4x'zi +4y'zj+3z*k, S is the sphere with radius R centered at…

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Q: Use the divergence theorem to calculate the flux of F = (x - 8y)i + (y – 4z)j + (z - 8x)k out of the…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = 7x3i +…

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

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2,…

A: The vector field is given as

Q: Use the divergence theorem to evaluate the flux of F(x, y, z) = 2xyi+ yzj+ z? k across the surface…

A: We will use Divergence theorem to evaluate the flux.

Q: Use the Divergence Theorem to find the flux of F = (xy², x²y, y) outward through

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Q: Use Divergence Theorem to evaluate the flux integral ∫∫F·ndS, where F = 〈x^2, y^2, z^2〉, S is the…

A: Divergence theorem:∫∫sF.⇀  N^dS =∬∫DdivF⇀dV , here D is the solid bounded by the closed surface S.

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (6x2…

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Q: Find the counterclockwise circulation and the outward flux of thefield F = (-sin y)i + (x cos y)j…

A: Use tangential form of Green's Theorem to find the counterclockwise circulation. Counterclockwise…

Q: Use the Divergence Theorem to calculate the flux of F across S, where F=zi+yj+zxk and S is the…

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Q: Use the Divergence Theorem to calculate the flux of F across S, where F = zi + yj + zxk and S is the…

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Q: Use the Divergence theorem to evaluate F. · dS where F (x, y, z) = (4x – z²) i+ (x+3z)j+(6 – z) k…

A: Using divergence theorem:  ∫∫SF.ds=∫∫∫V∇F.dv

Q: Let S be the closed cylinder bounded by the surface x? + z? = 4, and the planes y = 1 and y = 4. Use…

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Q: Use the divergence theorem to calculate the flux of F = (x - 9y)i + (y – 5z)j + (z – 3x)k out of the…

A: The divergence theorem mathematically states that:

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: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x³i + 3x²yj + 24xyk across the surface…

A: Flux of a vector field over a closed surface is equal to the divergence of the field in the volume…

Q: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…

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Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F =…

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

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Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…

A: By divergence theorem

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = 2xz i…

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Q: Use the Divergence Theorem to evaluate the flux of F = yi - xj + 2xk across the sphere x ^ 2 + y ^ 2…

A: Given: Fx,y,z=yi-xj+2xk  we want to calculate flux of Fx,y,z=yi-xj+2xk across the sphere x2+y2+z2=25…

Q: Use the Divergence Theorem to find the flux of F accross S; that is calculate LlF• nds where F(x, y,…

A: Topic : vector calculus

Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…

A: Solve the problem as shown below.

Q: Verify Divergence theorem for the function F = e,p over the semi-cylindrical volume { x* +y° sa…

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Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Use the Divergence Theorem to find the flux of F = xy2i + x2yj + yk outward through the surface of…

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Q: Find the flux of F across S, where F(x, y, z) = xyi + y²j + zk and S is the part of the paraboloid z…

A: According to question given that F(x,yz,)=xyi^ + y2 j ^+z k^S is the part of the paraboloid z=x2+y2,…

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

A: Given Fx,y,z=x2i^+xyj^+zk^=Pi^+Qj^+Rk^ bounded by the coordinate planes and 3x+4y+6z=24 Hence the…

Q: Verify the Divergence Theorem for the F(x,y,z) = 4xi +4yj +2z? k over the surface S of x² +y² and z…

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