Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x^2 + 3xz − y, 7y^3 − 6y, 9x^2 + 4z^2 − 3x outward from the region F that lies inside the sphere x^2 + y^2 + z^2 = 25 and outside the solid cylinder x^2 + y^2 = 4 with top at z = 1 and bottom at z = −1.

Q: Find the flux of the vector field F(x, y, z) = 3xi+3yj+6zk across the portion of the surface z = 25…

A: The flux F across the surface is given by ϕ=∫σF·nds=∬RF·∇GdA

Q: Calculate the divergence and curl for the following vector fields. Describe the characteristics of…

A: for a vector field F=P,Q,R Divergence  DivF=Px +Qy +Rz Curl of F =i^j^k^∂∂x∂∂y∂∂zPQR Divergence…

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

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z) across…

A: Given vector field F=x2,-y2,z2 D is the region in the first octant between the planes z=8-x-y and…

Q: verify the Divergence Theorem for the vector field and region. F(x, y, z) = (z, x, y), the box [0,…

A: Divergence Theorem states that : If F is continuous  differentiable vector function bounded by…

Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…

A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…

Q: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

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Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

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Q: Let = (xz, 2 4xyz, rz) be the velocity field of a fluid. Compute the flux of i across the surface…

A: Flux of velocity about a surface is the measure of amount of velocity of fluid hitting the surface.…

Q: (a) Verify the Divergence Theorem for the vector field and region: F = (5x, 6z, 5y) and the region…

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

Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Use the divergence theorem to calculate the flux of the vector field F = x3i - 3x2yj + 6zk through…

A: The divergence theorem is defined by the formula, ϕ=∮∂VF·ndS=∮V∇·FdV Consider the given vector…

Q: Find the flux of the vector field F = (x, z, - y) through the helicoid with parameterization r(u, v)…

A: Given :-  The flux of the vector field  F→ =  x3 , z , -y through the helicoid with the…

Q: Calculate the outward flux of the vector field F→ (x,y,z) = 2xi→ + yi→ +zk→ along the boundary of…

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Q: Calculate the outward flux of the vector field F→ (x,y,z) = 2xi→ + yi→ +zk→ along the boundary of…

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Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: verify the Its Stoke For Upper Projection theorem Vector Field F = (2x-y)i - yzj- y²zK ² Surface the…

A: To verify Stoke's theorem: For a vector field F=(2x-y)i-yzj-y2zk over the upper half of the surface…

Q: Define the force field ₹(x, y, z) =. Let S be the portion of the plane z = 2 - 2x in the first…

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Q: Why does a two-dimensional vector field with zero curl on aregion have zero circulation on a closed…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z") the…

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Q: Suppose a particle travels clockwise on a triangular path connecting the points (0,0), (3,1), and…

A: greens theorem

Q: Evaluate line integral of vector field F(x, y, z) = y sin(x²) i+ xyz j+ (x +y + z) k along line…

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: I have solution for 1

Q: Verify the Divergence Theorem for the vector field and region: F = (6z, 2z, 7y) and the region r? +…

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Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D…

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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 flux of the vector field F = (3x2 – 3yz + 423) i + (4.xz –…

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Q: Verify the Divergence Theorem: ls F- dS where F= (3z + z",y – sin zz, 2z+ ye) and Sis surface of box…

A: We need to find integral using divergence theorem.

Q: Consider the surface S consisting of the part of the cone z =5- vx + y² above the plane z = 0,…

A: Given the vector field F→=x33,y33,0. The surface S is bounded by z=5-x2+y2,z=0,x2+y2≤25. The formula…

Q: Verify the Divergence Theorem for the vector field and region: F = (4x, 6z, 8y) and the region x² +…

A: Solution

Q: Show that the vector field F = 2xyi +(x² - 2y)j is conservative and evaluate the line integral (F•dš…

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Q: Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface…

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Q: Verify the Divergence Theorem for the vector field and region: F= (4x, 8z, 4y) and the region x +…

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Q: 4. Verify that the two integrals in the circulation form of Green's Theorem are equal along a circle…

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: According to the divergence theorem:

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence

A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: "roblem #5: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

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Q: Calculate the vector field flow F(x,y,z)=(x2,y2,z2)  through S, where S is a flat surface x+y=2,…

A: To evaluate ∫∫SF.dS: By the divergence theorem, ∫∫SF.dS=∫∫∫Ediv F dV where E is the solid enclosed…

Q: Calculate the vector field flow f➝ (x,y,z) = (xy, y2, z) through the outer surface of solid T in the…

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Q: diverge

A: answer is in next step