1 Let G(x, y, z)= (1+9xy)² and consider a surface S given by the parametrization r(u, v)= [u, u³, v], 0
Q: 6. For any closed surface S, prove that || CurlF.N dS=0.
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Q: 6. Sketch the surface described by the parameterization r(u, v) = (u, v cos(u), v sin(u)) for 0 ≤ u≤…
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Q: b) Given F(r, y, z) = (x³ + cosh z) i+ (2y - 3ry)j – (x² + 4y²z) k. Use %3D Gauss's theorem to…
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Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).
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Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?
A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is Option C is correct.
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Q: Use Stokes' Theorem to evaluate fF.dr where F(x, y, z) = zi − 3yzj+ xk and C is the boundary of the…
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Q: 12. Let C represent the curve of intersection between the cylinder x² + y² = 4 and the plane z = 10…
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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 22²yk. %3D div F=|2 + 12 y² x² + 4 z y curl F=|2…
A: Find div F and curl F
Q: 1. Parametrize the following surfaces: (a) The portion of the plane x+y+z = 1 which lies in the…
A: a)Portion of the plane in the octant:Since we want the portion in the first octant, we can use the…
Q: Match the parametrizations to the surfaces shown in the figures. Þ(u, v) = v 4² u cos(v) (u, U) = |…
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Q: 31. Use Stokes' theorem to evaluate curl F. ds, where F(x, y, z) = −y² î + x + z²k and S is the part…
A: Given: F⇀x, y, z =-y2 i^+xj^+z2 k^ , x+y+z=1 , x≥0 , y≥0 ,z≥0. To find: ∬S curl F⇀·dS
Q: 1 Vø – ¢V 1 I = · d.5, - ||R – Ro| where S is the surface of the sphere (x – 1)2 + (y – 2)² + (z –…
A: Let s is the surface of the sphere x-12+y-12+z-32-64=0R→=i→+j^+k^Let,ϕ=x-12+y-12+z-32-64=0Then…
Q: b) Given F(r. y. :) = (r* + cosh : )i+(2y – 3.r"y) j - (r + 4y:) k. Use Gauss's theorem to calculate…
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Q: 5. Given that F = xzi– 2yzj+x²yzk Find the followings at (1, 1, 3): (a) div F. (b) curl F. (c) ▼·(V…
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Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…
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Q: 3. Let H = 2xi – 3xy j+xz² k. Calculate ſ, Ĥ •d where S is the surface of the cube with corners at…
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Q: 1. Let S be the portion of the surface x² + z² = 1 lying in the first octant and bounded by x = 0, y…
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Q: 6. Let S denote the disc of radius 2 that is centered at the point (0, 0,3) and parallel to the X-Y…
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- (c) Let S be a surface described by x² + y² + 3z² = 1, z ≤ 0, and let F(x, y, z)= yi aj+zx³y²k. Prove that √(V x 1 (V x F) dS = 2π9. Let S be the surface parametrized by (u, v³, u + v) where 05. Verify Stoke's Theorem for F(x, y, z) = (3y, 4z, −6z) and S is the part of the paraboloid z = 9x² - y² that lies above the xy - plane with outward facing normal. (a)Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,