Find the flux of F across S, where F(x, y, z) = xyi + y²j + zk and S is the part of the paraboloid z = x2 + y? below the plane z = 2 with upward orientation.

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: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (5x3…

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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: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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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: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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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: 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: 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: Let S be the portion of the cylinder y² + z² = 4 with z > 0 between the planes r = 0 and a = 5…

A: To compute the flux of below function F across S F=x2,y2,z2

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 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: Calculate F- dS where F = (3zy', ze", z) S is the surface of the solid bounded by the cylinder y? +…

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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 the divergence theorem to compute the value of flux integral F. dS, where F(x, y, z) = 5yj - 5zk…

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Q: 4. Use divergence theorem to find the flux of F(x, y, z) = x² yî – xy²ĵ+(z+2)k; o is the surface of…

A: Consider the given vector field, F→x,y,z=x2yi^-xy2j^+z+2k^ bounded above by the plain z=2y and below…

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: 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: 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 the Divergence Theorem to find the outward flux of F across the boundary of the region F = (6x2…

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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: 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 outward flux of F= (x')i+(y²)}+(z²)k across the boundary of the region D, where D 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: 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: 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: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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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: Calculate F- dS where F = (3ry², re², z³) S is the surface of the solid bounded by the cylinder y? +…

A: The general form of a vector-valued function in three dimensions is given by F¯=F1,F2,F3, where F1,…

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, 2) = (r, y, 2) across the surface o which is the surface of the solid…

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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: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

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 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: 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…

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.