IS² F(x, y, z) = xyezi + xy²z³j - yek, S is the surface of the box bounded by the coordinate planes and the planes x = 3, y = 4, and z = 1 Use the divergence theorem to calculate the surface integral F. ds; that is, calculate the flux of F across S.

Q: Let z g(x, y) = f(3 cos(xy), y + e#v) provided that f(3,5) = 4, f1(3, 5) = 2, f2(3, 5) = 4. i) Find…

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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: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

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Q: Let z = g(z, y) = f(3 cos(ry), y + e") provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) = 3. i)…

A: Let z=gx,y=f3cosxy, y+exy f3,7=4, f13,7=2, f23,7=3

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

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Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

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 z = 9(x, y) = f(3 cos(xy), y + e™y) provided that f(3,7) = 4, fi (3, 7) = 2, f2(3, 7) = 3. i)…

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Q: Let z = g(x, y) = f(3 cos(xy), y + ev) provided that f(3,6)= 7, f₁(3,6) = 2, f₂(3,6)= 5. i) Find g₁…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: 4. Let F(r, y, z) =-ri+ yj + zk and o be the portion of the surface z = 8x-² - y? that lies above…

A: Given vector field is  F(x,y,z)=43xi+43yj+53zk and also the surface σ is portion of the sphere…

Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

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Q: tz = g(x, y) = f(3 cos(xy), y + e#") provided that f(3, 7) = 4, f1(3, 7) = 2, (3, 7) = 3. %3D Find…

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Q: Find g, (0,3). ) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3…

A: 1st option is correct

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

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Q: Let z = g(x, y) = f(3 cos(xy), y+ e#y) provided that f(3,6) = 6, f1(3, 6) = 2, f2(3, 6) = 5. i) Find…

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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: Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane…

A: We have to find the flux F(x,y,z)=2xi+2yj+zk across the point of the paraboloid z=4-x2-y2 above the…

Q: Evaluate the line integral by stokes theorem where F(vector)=[ 0, xyz ,0] , C is the boundary of a…

A: Calculate curl:  curlF=ijk∂∂x∂∂y∂∂z0xyz0         =i-xy+kyz

Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

Q: (1) Let F(r, y, z) = (y², e², z). (a) Compute the divergence of F. (b) Use the divergence theorem to…

A: Answer

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: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

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Q: i) Find g1 (0, 4). ii) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z…

A: Since g(x, y) = f(3cosxy,y+exy)

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) i) Find g1…

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