Find the flux of F(x, y, z) = (e² + 2x, 3x², y) across the surface S defined by R(u, v) = (u², uv, v), where 0 ≤ u≤ 1,0 ≤v≤ 2. parametrically

Q: Compute the flux of F¹ = 5(x + z)i + 5j + 5zk through the surface S given by y = x² + z², with 0 ≤ y…

A: The given surface is  and .The flux is given by  where  is the vector function that describes the…

Q: 4. Find the flux of F across S if F = yi-xj+2zk and S is the hemisphere x² + y² + z² = 4, z ≥ 0,…

A: We have to find flux passing through sphere.

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: Draw the parameterized surface

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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: 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: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h>0z=0 Also F→=x2, y2, z2 To…

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 2r + 3y –= 5 be the tangent plane to a surface z = f(r,y) at the point (1,1). (a) Find the…

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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: Use Green's t'heorem to find the work done by the overline force P (z,y) = x({s+y}stay when moving a…

A: see my solution

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: 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: 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: Let z = g(x, y) = f(3 cos(ry), y + e²") provided that f(3,5) = 7, f1(3,5) = 2, f2(3, 5) = 5. i) Find…

A: The function given z=gx,y=f3cosxy,y+exy;f3,5=7,f13,5=2,f23,5=5. i. Find g10,4

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: 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: Compute the upward flux of F across the surface defined by R(u,v) = where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 1.

A: The given surface is Ru, v=<2u, 3v, u2-v2>.......(i), where 0≤u≤2 and 0≤v≤1 and F→x, y,…

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 F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

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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: 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: 1.The electrical voltage in a certain region is given by V(x,y,z) = 5x² -2xy + xyz. a) Find the rate…

A: Gradient of a Function:   Let f(x,y,z) be a function in ℝ3. The gradient (denoted by ∇f) is given by…

Q: a) Letfx, y) = xe-y+ 5y.Find the slope of the surface z = fx, y) in the y-direction at the point (3,…

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

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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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Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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