Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F dS where S is the top half of the sphere z? + y? + z? = 1 oriented upwards. SSF. dS =

Q: Calculate F · dS where F = (e* sin cos y, yz?) y, et and S is the surface of the box bounded by the…

A: By using the divergence theorem, we can make equality between the surface integral of a function and…

Q: Using the Divergence Theorem, evaluate I= F dS where S is the sphere of radius 2 centered at the…

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Q: 7.H Jse the divergence theorem to evaluate where S is the sphere x+y? +? = 4 oriented with outward…

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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: Let (r, y, z) 2 F := + y2 + and let S be the boundary of the sphere x2 + y² + z2 = 1 oriented…

A: Divergence theorem: Let D be a simple solid region and s is the boundary surface of D. Let F→ be a…

Q: Evaluate fs F dS, where F(r, y, z) = (2², xy, z) and S is the part of the paraboloid z = 22 + y?…

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Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: Use the divergence theorem to evaluate ]] F .dɔ̃ where F = xyi – ¹⁄y²j+zk and the surface consists…

A: Here, the surface consists of the three surface z=4-3x2-3y2; 1≤z≤4 on the top x2+y2=1, 0≤z≤1 and z=0…

Q: Use the Divergence Theorem to evaluate F. dS where F = (2²a +y?. + tan (2), a?z – 1 2, and S is the…

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Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

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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 Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Use Stokes' Theorem to evaluate F. dr, where F (x, y, z) = zi + yj – xk and C is the boundary of the…

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Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

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: b) Use Gauss' theorem to evaluate f[ F· ndS where M UTM = (x² – y)i + y°z²j + (xy – y²z³)k and o is…

A: The given problem is to evaluate the given double integral using gauss divergence theorem over the…

Q: Verify the divergence theorem, ffaw F · dS = S[fw, Div FdV, for F(x, y, z) = (z)i + (y)j + (x)k,…

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Q: Let S be the portion of the paraboloid z = r² + y? below z = 4 together with the disk a2 + y² < 4 in…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = z³ i –x³j+ y° k across the sphere x? +…

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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: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

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Q: Let F=[x+y, y+z, x+z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Topic- vectors

Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

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Q: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

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Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + 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: 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: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = zi + yj – rk and C is the boundary of the…

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Q: Verify the Divergence Theorem SI div F av F. dS S E for F(r,y,2) = z i+ yj+xk and where E is the…

A: Given that Fx,y,z=z i+ y j +x k and E is the solid ball x2+y2+z2≤16. First find the divergence of F.…

Q: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

A: We will find out the required value.

Q: V9/ Compute I ,cxyz), uhere s is the part f the plane +x that lies inside the half - cyllnder…

A: Given: The Integral is ∬SxyzdS. The surface is the part of the plane S  z=y+x that is inside the…

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

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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: Use the Divergence Theorem to evaluate the surface integral |a? – 3y + 62) ds, S. here S is the…

A: Given the surface integral ∬Sx2-3y+6zdS, where S is the sphere x2+y2+z2=9. The integrand is a scalar…

Q: Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) ·…

A: a) Given the field, F=2x+yzi-2yj+z2+xk The surface S is the sphere x2+y2+z2=4 with an outward…

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

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Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: Use the Divergence Theorem to evaluate  F · dS,  where  F(x, y, z) = z2xi +  + ((1/3)y3 + cos z)j +…

A: Given data:

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: Let F(x, y, z) = (x,y,z). Compute ∫∫sF · dS where S is the part of the plane x + y + z = 1 in the…

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Q: Calculate F. dS where F = (e sin Y, cos y, yz?) S is the surface of the box bounded by the planes x…

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Q: Find the circulation of F(x, y, z) = (-ysin z, x sin z, xy cos z + 12) around the circle cut from…

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Q: Let S be the upper surface of the sphere x- 2x+y+z = 0 and let r be the boundary. Find [.curi(F) -…

A: S is upper surface, the equation  x2-2x+y2+z2=0  x-12+y2+z2=1  Hence, is a sphere centered at (1, 0,…

Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.