The flux of F(x, y, z) = 2³î – r³}+ y®k, where o is the sphere | x2 + y? + z2 = a² with outward orientation by using the Divergence :Theorem is

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

A: Solved below...

Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Calculate F - dS where F (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the planes…

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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: Verify the formula J.F., F.ndS= =JJJ₂ div div F dV G in the Divergence Theorem by evaluating the…

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Q: Find the flux of F across the oriented surface S by evaluating the surface integral F.î dS. F = zî +…

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Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: Use Divergence Theorem to evaluate ,0²z²i + z²x²j+ x²y²k).ds, 1. where S is the upper part of the…

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Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

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: Use Divergence Theorem to evaluate .(v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: Gauss Divergence Theorem : ∫∫SF·ndS=∫∫∫VdivF dV From ∫∫Sy2z2i+z2x2j+x2y2k·dS, F=y2z2i+z2x2j+x2y2k

Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Use divergence theorem to evaluate F •dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

A: According to the divergence theorem ∬SF¯·ds¯=∫V∇·F¯dV, where V is the volume bounded by the closed…

Q: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Apply the divergence Theorem,with the surface of F = 4xzỉ – y²j + yzk and S being the cube surface…

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: Use the Divergence Theorem to evaluate (6x + 7y + z2) dS where S is the sphere x2 + y2 + z? = 1.

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

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Q: Use divergence theorem to evaluate F·dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

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Q: Use Divergence Theorem to evaluate [0²z?i+z?x²j+x*y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral using the divergence theorem. ∫∫Sy2z2i+z2x2j+x2y2kds Here S is the…

Q: Q5. Analyze and Verify Gauss divergence theorem for F 2 xz i+ yzj+ z? k over the upper half of the…

A: Here, F=2xzi+yzj+z2k Given upper half of the sphere x2+y2+z2=a2. Let ∅=x2+y2+z2-a2=0…

Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

Q: 5. Compute / | F. aš, where F = (y, -x, 2z) and S is the surface of the sphere of radius 2, centered…

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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: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Use the Divergence Theorem to evaluate F. dS , where F(r, y, z) = (2x(y - z), x? – y, z) and S is…

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Q: Find the flux of F(x, y, z) = (z, 4x, y) through the surface S, when S is the part of the plane 2x +…

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Q: Use Divergence Theorem to evaluate .v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral. ∫∫sy2z2i+z2x2j+x2y2kds¯

Q: Let F(x, y, z) = 2z? xi + (y + tan(z))j + (2x²z – 2y²)k. Use the Divergence Theorem to evaluate F.…

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Q: evaluate.both sides of divergence theorem for A= ra,+rcos(e)a, +ra, through the closed surface…

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Q: Use the Divergence Theorem to evaluate (3x + 2y + z2) ds where S is the sphere x2 + y2 + z² = 1.

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

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Q: Integrate g(x,y,z) = x + 5y + z over the portion of the plane 4x + 8y + z = 8 that lies in the first…

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Q: find the flux of f=zk across the portion of the sphere x2+y2+z2=a2 in the first octant in the…

A: Given the field, F=zk The surface S is the portion of the sphere x2+y2+z2=a2 in the first octant in…

Q: Use the Divergence Theorem to evaluate (4x + 7y + z²) dS where S is the sphere x2 + y2 + z² = 1.

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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: Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

A: The divergence theorem establishes the equality between surface integral and volume integral.

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

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Q: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: Use the Divergence Theorem to evaluate where F = (xy + z)i+ (zy)i+ (x+z)k and the surface consist of…

A: The function given is F→=xy+zi^+13xy3j^+x+zk^. The closed surfaces are as follows: z=4-3x2-3y2,…

Q: se the Divergence Theorem to evaluate (8x + 12y + z2) ds Is here S is the sphere x2 + y2 + z² = 1.

A: To compute the below integral using divergence theorem.

Q: Verify the formula F-nds = | div F dv in the Divergence Theorem by evaluating the surface integral…

A: Given that Fx,y,z=2xi→-yzj→+z2k→ Where σ is the paraboloid z=x2+y2 capped by the disc x2+y2≤16 in…

Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: Evaluate both sides of divergence theorem for A= pa, + pcos(0)a , + zaz through the closed surface…

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Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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