Find the flux of F(x, y, z) = (z, 4x, y) through the surface S, when S is the part of the plane 2x + y + z = 4 that lies in the first octant, oriented upwards.

Q: find the outward flux of F across the boundary of D. F =-2x i - 3y j + z k D: The upper region cut…

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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: Find the flux of F(x, y, z) = 4а, 32 + 2?, across the positively oriented surface 2 S given by R(u,…

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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 find the flux of F(x, y, z) = (x – z)i+ (y – x)j+ (z – y)k - across…

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Q: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

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: Let S be the cylinder x +y a, 0szsh, together with its top, x +y sa, z=h. Let F= -7yi + 7xj + 7x k.…

A: Given data: S is the cylinder, with its top x2+y2≤a and height0≤z≤h. Also Given a vector F→ Such…

Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from 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 calculate the flux of Flacross SI where F = zi + yj + zxk|and Slis the…

A: Given that F=zi+yj+zxk And, The objective is to find the .

Q: The outward flux of F(x, y, z) = xi + yj + zk across any unit cube is.

A: Given flux is F=xi+yj+zk. Compute div F. divF=∂∂xx+∂∂yy+∂∂zz=1+1+1=3

Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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Q: Use a parametrization to find the flux I F.n do across the surface in the given direction. F= - xi -…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i + (y – x)j+ (z – y)k %3D -…

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Q: Find the outward flux of F through S. F-Ñ dS where F(z, y, z) = -3zî+y³j+yk, and S is the surface of…

A: The general form of a vector valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

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 evaluate F.N ds and find the outward flux of F through the surface of…

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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: Let F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…

A: The given problem is to find the flux of vector field over the given surface of part of the…

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F across S, the part of the…

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Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

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 a parametrization to find the flux F•n do across the surface in the given direction. F= - xi -…

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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: Find the flux of F across S, where F(x,y,z) = xˆi + yˆj + zˆk and S is the part of the cone z = √x2+…

A: Surface integral problem

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 4)j + zk. Find the flux of F across S, the part of the…

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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: Let F(x, y, z) = z tan¬1(y²)i + z³ In(x² + 9)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) = 3x³i + 3x²yj + 24xyk across the surface…

A: Flux of a vector field over a closed surface is equal to the divergence of the field in the volume…

Q: Find the circulation of F= (xy)i+(yz')j-(2xyz)k around the curve C in the counterclockwise direction…

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Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

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Q: Evaluate F-N dS and find the outward flux of F(z,y, z) = ryî+yzj-yzk, through %3D the surface S of…

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Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2 i…

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Q: oriented

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Q: Find the flux of F(x, y, z) = x sqrt(x^2 + y^2) i + y sqrt(x^2 + y^2) j + z k through the portion of…

A: Introduction: - Let F be a function and let the region isS, then the flux of the function is given…

Q: Use divergence theorem to find the flux of F(x, y, z) = x² yì – xy² j+ (z+ 2) k ; o is the surface…

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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: Find the flux of F = (y +xz)i + (y + yz)j – (2x + z²)k upward through the first octant part of the…

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Q: Let F(x, y, z) = z tan-1(y²)i + z³ In(x² + 1)j + zk. Find the flux of F across S, the part of the…

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Q: Let F(x, y, z)= (sin (zy))i +(z° cosh x)j+(z² )k. Find the flux of F across the positively oriented…

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Q: Let S be the piece of the surface z = 9-r that lies inside the cylinder r2 +y² = 9, and let F = (x,…

A: Given, S be the piece of the surface z=9-x2 that lies inside the cylinder x2+y2=9, and let F=x,y2,z.…

Q: Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of…

A: Given Fx,y,z=x2i^+xyj^+zk^=Pi^+Qj^+Rk^ bounded by the coordinate planes and 3x+4y+6z=24 Hence the…

Q: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

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: Find an equation for the plane through the origin such that the circulation of the flow field F = zi…

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Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F across S, the part of the…

A: Given that    Fx,y,z=z tan-1y2i+z3Inx2+6j+2k Also, the part of paraboloid x2+y2+z=6 that lies above…