Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D (-5х2 + 3xz - у, 4у3 - бу, 9х2 + 422 - 3х) outward from the region F that lies inside the sphere x2 + y? + z2 = 25 and outside the solid cylinder x + y? = 4 with top at z = 1 and bottom at z = -1.

Q: Find the divergence of the vector field F <7", 22°, zy* div F -

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

A: The surface integrals compute the flux of fields across surfaces,                   So,…

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: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…

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Q: Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

A: The answer is as follows:

Q: A vector field is described as F = (-z + 7x, x³y²z=1,3x + 2z²). (i) Calculate curl F. (ii) Determine…

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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: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

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 divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: Why does a two-dimensional vector field with zero divergence ona region have zero outward flux…

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

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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: Compute the flux of the vector field (x, - xy*), out of the rectangle with vertices (0,0), (5,0),…

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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: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

Q: Compute the flux of the vector field F = 3xzi + 5yk through the surface S, which is the hemisphere…

A: The flux is given byflux =∫S  F→·n^  dShere,n^=x, y, zx2+y2+z2 in spherical coordinatesF→·n^ =x, y,…

Q: 1. Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

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

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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: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Let the given vector field is :

Q: Find the divergence of the given vector field at point (1,1,1). Insert your answer below. Round to…

A: Fx, y, z=3x2yi+2xz3j+y4k Comparing with F=Pi+Qj+Rk, we get P=3x2y,  Q=2xz3,  R=y4 Now, ∂P∂x=∂3x2y∂x,…

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

Q: How is the circulation of a vector field on a closed smooth orientedcurve calculated?

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Q: ul for the through the box [o,8] x[ 0,41 x[0,2]. vector field f=<z,x, y2, calculate the rotalflux S.…

A: We need to calculate divergence . The formula for divergence for F=&lt;P,Q,R&gt; is ,…

Q: Verify Stoke's theorem for the vector field F = (2x - y) I- yz*J-yzK over the upper half surface of…

A: Stokes theorem is used

Q: The divergence of the vector field F(z, y, z) = (ya°, az", zy?) is: %3D

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Q: . Verify Stoke's theorem for the vector field F = (2x - y) I– yz²J -y z K over the upper half…

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Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

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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: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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Q: Let W be the region between the sphere of radius 4 and the cube of side 1, both centered at the…

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Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

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: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

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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: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: Let divF(x, y, z) 4x3 + 4y3 + 4z³ , where F represents the flow of a vector field. Estimate the flux…

A: Given that a small sphere of radius 0.1, centered at the point  (1, 1, 1).And                  div F…

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…