Set up the surface integral for Stokes' Theorem to find F dr given th F(x, y,z)= (xʻz, xyz, xsin y) where S is the oriented first octant portion of 4 %3D all information required by Stokes' Theorem as demonstrated by our instruction. Do I

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Q: Evaluate the line integral (2 yi + (r- 2)j+ zyzk) · dr where C is the parametric curve r(t) = ti +…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: We have to find

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: Consider the circle in the ay-plane given by the parametrization x = 2 cos t, y = 1+2 sin t, 0<t<…

A: Let's find.

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…

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Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² 10 at point…

A: We have to calculate partial derivatives first.

Q: SS curl F · dS =0 S

A: we have to prove that if a surface is closed then the surface integral of curlF .ds is 0 Here…

Q: Use Stokes' Theorem to calculate rot F dS, where F = ri + yj + rk and S is the surface given by the…

A: This is a problem of vector calculus. By using stokes theorem formula we will evaluate given…

Q: Find the equation of the tangent plane Pr to the surface S:x2 +y? + z2 = 9 at (2,-1, 2)

A: To find :Equation of tangent plane to the surface x2+y2+z2=9 at the point (2,-1,2).

Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = 2²i + 26xj – y°k | where C is the circle x2 + y²…

A: The objective is to find ∮CF.dr using Stoke's Theorem. Where F(x,y,z)=z2i+26xj-y3k and C is the…

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