a. Use the Divergence theorem to calculate ff (vn) do for v(x, y, z) = (x+z)i + (y+z)j + (x+z)k on the surface S: y² +2²=1, 0≤x≤4 b. Calculate the total flux of v(x, y, z) = 2xi+xz j+z²k out of the solid bounded by the paraboloid z = 9-x² - y² and the xy-plane.

Q: Use the Divergency Theorem to evaluate F. Nds and find the outward flux of F through the surface of…

A: F(x,y)=(xy2+cosz)i+(x2y+sinz)j+ezkS:z=12x2+y2,z=2. By using Divergence theorem to evaluate the…

Q: The solid E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4, and within the cone z =…

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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: 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: Suppose F(x, y, z) = (y, x², 3) and suppose S is the surface parametrized by r(u, v) = (u, 3+v, 2 −…

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Q: Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation…

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Q: Suppose F(x, y, z) = (x, y, 52). Let W be the solid bounded by the paraboloid z = x² + y² and the…

A: Given:  F→x, y, z=x, y, 5z Paraboloid z=x2+y2 Plane z=25 To find:  a ∬S F→·dA→ b (i) Flux out of the…

Q: 6. Find the total upward flux of F(x, y, z) = yi + xj + zk over the surface o: z = 1 - x² - y² above…

A: Given: F(x,y,z)=yi+xj+zk           Surface,σ:z=1-x2-y2 To find: The total upward flux of F(x,y,z)…

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

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

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Q: 16. Use the Divergence Theorem to find the total outward flux of F = xi + 2yj + 3zk across the…

A: We have to use the divergence theorem and find out the outward flux of  F=xi+2yj+3zkAcross the…

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

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Q: 1. Aflock of birds is perched on a tree branch. The branch B can be modeled as a 3-D line segment…

A: We have to parametrize the branch B and evaluate the integral.

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 the Divergence Theorem to evaluate [/F. F-N ds and find the outward flux of F through the…

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Q: Find the flux of F = yi + 2zxj – z²k through the parabolic cylinder y = x2,0 < x < 1,0 < z< 4, in…

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Q: 2. Consider the second-order differential equation d²x dx +a + b²x = 0 (a, b positive real…

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Q: Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the…

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Q: b) Given F(.r, y. :) = (r + cosh 2)i+ (2y-3r*y)j-(r + 4y*:) k. Use Gauss's theorem to calculate F.n…

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Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the flux of the disk…

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Q: Let F(x, y) = (xy² + 7x, x²y-7y). Compute the flux F nds of F across a simple closed curve that is…

A: It is given that the vector field is . Let  then wehave,  and .We have to compute the flux  of the…

Q: Compute the flux of F (x, y, z) = (y, z, x) across the surface S : R(u, v) = (u+2v, v – u, u), where…

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Q: Find the flux of F

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Q: Suppose C is a constant vector. Let F(x, y, z) = C find the flux of F through a surface S on plane…

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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…

A: The given vector field is F(x,y,z)=x2 i +y2 j +z2 k and S: x=0, x=a, y=0, y=a, z=0, z=a.  To…

Q: 3. Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the…

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Q: Let S₂ be the portion of the paraboloid z = 9-4x² - 4y² on the first octant above the plane z = 1.…

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Q: Let F(x, y, z)=zi+yj+z¹k. Compute the flux of F over the surface S, which is the part of the cone z…

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Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Let F(x, y, z) = z tan−1(y2) i + z3 ln(x2 + 8) j + z k. Find the flux of F across S, the part of the…

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