Let (r, y, z) 2 F := + y2 + and let S be the boundary of the sphere x2 + y² + z2 = 1 oriented outwards. Consider the flux of F through S: F ·dS = Añ. Use the divergence theorem to find A =

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: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

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 calculate the surface integral F. dS; that is, calculate the flux of 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 = y…

A: The divergence theorem states:

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

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 flux of F(x, y, z) = (x² + y)i+z°j+ (e° – z)k across the…

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Q: Let E be the solid bounded by the xy-plane and paraboloid z = 4 - x2 - y2 so that S is the surface…

A: According to question, Paraboloid z =4-x2-y2,Fx, y, z = xz sinyz + x3 i + cosyz j + 3zy2-ex2 +y2 k

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: 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 calculate F.dS, where F (x, y, 2) = x² yzi + 2yzj – xyzk and %3D S is…

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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 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: Let F(x, y, z) = z tan-1(y?)i + z In(x2 + 8)j + zk. Find the flux of F across S, the part 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 calculate the flux of the vector field F(x, y, z) = x°i + (5y – 5x*y)j…

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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…

A: See the details solution in below

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 find the outward flux of the vector field F(x, y, z) = 7x3i +…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = xy2i + yz2j +…

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Q: Use the Divergence Theorem to calculate the surface integral || F. dS; that is, calculate the flux…

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Q: Let F = (zy, y + x²z,3z2 – yz), let E be the cube [0, 1] × [0, 2] × [0,3] in R³, let S be the…

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Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

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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: Consider the force fields F,(x, y) = (y² + 2xe", x(3y+ xe + 1)) and F2(x, y) = (M, N). Let C be the…

A: For a vector field F=Pi +Qj ∮CF.dr=∫C(Pdx+Qdy) If curve C enclosed the region A ,  By greens theorem…

Q: Use the Divergence Theorem to calculate the surface integral Sl. F. dS ; that is, calculate the flux…

A: We will find out the required value.

Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Use the Divergence Theorem to calculate the flux [fF . d§, where F(x, y, z) = (1) (sin(yz) + yz)i +…

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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 find the flux of F(x, y, z) = 3x°i+ 3.x²yj+ 33xyk across the surface…

A: According to the given information, it is required to use the divergence theorem to find the flux.

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 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 find the outward flux of F across the boundary of the region D. F=x°i-…

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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: 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: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across ơ, where o is the portion of the…

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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: Let F = [a2,0, 22), and S the surface of the box |r| < 1, |y| < 3, 0 < z < 2. %3D -face integral F.n…

A: The divergence of the function F is:

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: Use the Divergence Theorem to calculate the surface integral F• ds; that is, calculate the flux of F…

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Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: Let F(x, y, z) = z tan-(y2)i + z³ In(x2 + 9)j + zk. Find the flux of F across S, the part of the…

A: Get points of intersection of the paraboloid and z=3:  Thus, point of intersection is a circle in…

Q: Use the Divergence Theorem to calculate the Flux of F(x,y, z) = 1xi+ 5yj+ 2zk, E is the surface of…

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Q: Use the Divergence Theorem to determine the value of f f, F•dS where F (x, y, z) = (3x – x² )i+…

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Q: Calculate the flux of F across G. F(x, y, z) = 2xi + 2yj + 2zk; G is the surface of the sphere x2 +…

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Q: Use the Divergence Theorem to calculate the outward flux of F = rr| where r = (r, y, z) across S:…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = x³i + y³j+ z³k…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.