Let F =i+x^2j, and let C be the boundary of the region {(x, y):x^2 + y^2 ≤ 1 and x ≥ 0}: the right half of the unit disk. Find the outward flux of F across C.

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Let Ġ(x, y) = (x², y). Calculate the flux of G across the line segment from (0, 0) to (1, − 2).

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Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

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

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The given vector field is F→=xi+yj+zk. The goal is to evaluate the flux or surface integral of the…

Q: Calculate the flow of F(x, y, z) = (y², x, x²) across the surface z = 4-x²-y² above the z = 1 plane

A: The field is F→(x, y, z) = y2, x, x2. The surface is . Then fx, y, z=z+x2+y2-4 Obtain the normal:…

Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

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Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

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Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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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 find the outward flux of F = (7x², et², cos³ (y² + x)) of the cube in R³…

A: Given that  and the cube  bounded by the planes The Divergence Theorem

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: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

A: Step 1:- To find the flux of the vector field F=(x2+y2+z2)3/2(x,y,z)​ through the given square…

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The vector field is F=xi^+yj^+zk^. The curves surface is x2+y2=1 bounded below by the plane x+y+z=2…

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Let F(x, y, z) = xzi+yzj + xyk, Surface S is the part of the sphere x² + y² + z² = 4 that lies…

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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: Use the Divergence Theorem to find the flux of F = (xy², x²y, y) outward through

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Q: Compute the flux of the vector field F(x, y, z) = 3i + 2j + 2k through the rectangular region with…

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Q: Let F(x, y, z)=(y)i +(x)j+(z³)k. Find the flux of F the positively oriented across closed surface S…

A: Here  ∇·F→ = 2x + 2y + 2z = 2(x+y+z) R.H.S = ∫∫∫V ∇·F→.dv R.H.S =…

Q: Let f(x,y,z) =x+y+z, let B be a ball of radius 1 around the origin,and let S be its surface a).…

A: GIVEN :-  Let f  x, y , z = x + y + z , let B be a ball of radius 1 around the origin , and let S be…

Q: Find the flux of F across S, 1.1. S F. N dS where N is the upward unit normal vector to S. F(x, y,…

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Q: Don't change the W subspace. It is  W = {(x,-x, 2x): x, y ≤ R}

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Q: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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Q: Show that U = {Ae² sin(3x): A = R} is a subspace of V.

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Q: t F (x, y, z) = (x + y²z, y³ + z³). Calculate the linearization of F at (1, 2,3).

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Q: Use the Divergence Theorem to evaluate the flux of F = yi - xj + 2xk across the sphere x ^ 2 + y ^ 2…

A: Given: Fx,y,z=yi-xj+2xk  we want to calculate flux of Fx,y,z=yi-xj+2xk across the sphere x2+y2+z2=25…