Use Divergence theorem to evaluate fs F.ndS where F(z, y, 2) = r'i+z'yj-+z°zk, n is the outer unit normal to S, and S is the surface enclosed by the cylinder 2r + y and the planes z 0 and z 2. Select one: O A: 167 OB. 87 OC 10

Q: →> Let S be the surface in R³ that is the image of the function F: R² R³ given by F(u, v) = (u²,…

A: The given surfaces are Fu,v=u2,v2,u+v and 2x2+y2+z2=7. To show that the point 1,1,2 lie on both the…

Q: For each of the parametric surfaces o given below and every pair of param- eters (u, v) in the…

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Q: Use Stokes's theorem to evaluate fFdRor (VxF) •nda where F(x,y,z)=x²-xy²j+2²k and I is the C…

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3…

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Q: For each of the parametric surfaces o given below and every pair of param- rs (u, v) in the domain…

A: Since you have posted multiple questions, as per the guideline, I am supposed to solve only first…

Q: F. dr where C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = xyi + 3zj + 5yk,…

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Q: J.F F = (e sin y, e cos y, yz²) S is the surface of the box bounded by the planes x = 3, y = 4, z =…

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Q: 3) Evaluate, to the nearest hundredth, 11. (V x F) dS where F = and S = {(x, y, z)| 2² − 1 = 3x² +…

A: Here we will use Stokes theorem  According to stokes theorem  ∫∫S∇×F.dS=∫CF.dr C is the  boundary…

Q: The work done by the force F = in the displacement along the path C:y=x² from the point (0,0) to…

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Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Let F(r, y,z) = where r2 + y? < 4, oriented by the upward normal. (r,-z,2y(r2-y²)). Find ff, F- dS…

A: Given Fx,y,z=x,-z,2yx2-y2and S is the saddle surface z=x2-y2, where x2+y2≤4, oriented by the upward…

Q: = Let x: R? → R³ be the function given by x(u, v) = (u cos v ,u sin v , bv) 1. Check whether x is…

A: (1)Given that:x:R2→R3 is the function given by x(u,v)=(ucosv,usinv,bv)In order to check the proper…

Q: (u, v) ~ (x, y) as (x, y) → (0,0) that will bring to the sum of squares z = A1u? + A2v² the…

A: given u=ux,yv=vx,y   and u,v~x,y as x,y→0,0 define a function z=λ1u2+λ2v2 where…

Q: F.N= (b) Calculate the normal component of F to the surface at P = (1, 2, 9) = (2, 3). (Use symbolic…

A: Given:It is given that  and  is the oriented surface parameterized by  for  and .To Find:(a) We have…

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Calculate F. dS where F = (4x°z, 4y*z, 32*) S is the surface of the solid bounded by the hemispheres…

A: Given that F→=(4x3z, 4y3z,3z4) and S is bounded by z=16-x2-y2, z=1-x2-y2, z=0 Now,…

Q: H.W Which of the following vectors is normal to the surface x?yz = 1 at (1,1,1)? (a) 4i +j+17k, (b)…

A: Given the surface is x2yz=1 and (x,y,z)=(1,1,1)

Q: r = 14,0 = I 4 Description of locus in (x, y, z) space: Line made by the intersection of the…

A: Given the Polar coordinates      r=14 and θ=π4 Find the Cartesian coordinate y.

Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u eR…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface