Given F(x, y, z) = -yzį + xzj – xyzk be a vector function that passes through a surface S of z +x? + y? = 20 that lies above z = 4, which is positively oriented. Sketch the surface S based on the given information, then evaluate ff, curl F n ds by using Stokes' Theorem.

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: We have to evaluate the surface integral ∬SydS Given vector equation is r→u,v=ucosv,usinv,v…

Q: F= (y, 2x, -z) and C is the circle x² +y² = 9

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Q: Calculate the surface integral / G(r) dA, where G = (12xz + 36)1/2, the surface S is given by the…

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Q: For vector A = , calculate the surface integral (f, A · ds)

A: In this question, we find the surface integral for the given vector function A=<x2yz, xy2z,…

Q: Use Stokes' Theorem to evaluate F dr where F = (x+ 9z) i + (5x + y) j + (7y- z) k and C is the curve…

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Q: Find the flux ofF across the oriented surface S' by evaluating the surface integral F.î dS. F = zî +…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Given F(x, y, z) = -yzi + xzj – xyzk be a vector function that passes through a surface S of z + x2…

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Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

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Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

Q: Consider x = h(y, z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: Suppose C is the curve parametrized by 7(t) = (cost, sin t, 1) and S is the portion of z = * + y…

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Q: #5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the…

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Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

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Q: Evaluate Curlv•ñ , where v = 2xyi + (x² – 2 y)] + xzk and ñ is a unit vector normal to the surface…

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Q: Attached picture is the question

A: Consider the provided question,

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = zeYi + x cos(y)j + xz sin(y)k, S is the…

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Q: Calculate the surface integral // y ds, where S is the part of the helicoid defined by the S vector…

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Q: Evaluate Curlv.ñ , where v = 2xyi +(x² – 2y)j + xzk and ñ is a unit vector normal to the surface…

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Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

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Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

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Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

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Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

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Q: Consider the set S given by S = {(x, y, z) ER³ : 2 = 2x² - y²}, where A E R\{0} is constant.…

A: As per the question we are given a quadratic surface as : S = {(x,y,z) ∈ R3 | z =2x2 - λy2} And we…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x? + y?…

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Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Let F (x, y, z): = (x + 2y2, y + z2, z + 2x2), and let C be the curve that results from the…

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Q: Let us verify Stokes' theorem using the vector field F = (x 2 - y)i + 4zj + x 2k, where the closed…

A: We are given a 3d vector field and a cloced conture, using which we have to justify the Stoke's…

Q: Use Stokes' theorem to evaluate curl(F) · dS. F(x, y, z) = x² sin(z) i + yj + xyk, S is the part of…

A: Given that, And he paraboliod is The aim is to find The radius is 3. Take C is x(t)=cos t and…

Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

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

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

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Q: Find the surface normal vector to the surface z 4-(x +y²) at the point (1, 1,v2) by (a) Vf (b) N =…

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Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: Given F(x, y, z) = -xị + yzj + xyzk be a vector function that passes through a surface S of z+x² +…

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Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

A: We are given that S is a square plate with boundary C, having each side of length 2 units, lying in…

Q: (4) Use Stokes' Theorem to calculate the work-done by the force field F(r, y, z) = (x² + z²)î + (y²…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: Use Stokes' theorem to evaluate curl(F) · ds. F(x, y, z) = exYi + ej + xzk, Sis the half of the…

A: Given: F(x,y,z)=e4xy i+exz j+x2z k The half of ellipsoid 8x2+y2+8z2=8 To find:  ∫S∫curl(F). dS Use…

Q: iv) Given F (x, y, z) = -yzį + 2xj + xyzk be a vector function that passes through a surface S of z+…

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Q: Use Stokes' Theorem to evaluate|| curl F. dS. F(x, y, z) = x²y³zi + sin(xyz)j + xyzk, S is the part…

A: The vector field is Fx, y, z=x2y3zi+sinxyzj+xyzk Find: ∫∫Scurl F·dS Then, the double integral…

Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an…

A: Given that F(x,y,z)=xi+zj+2yk    ….(1) The equation of cylinder and plane is x2+y2=1  and z=x…