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- Compute the surface area of the surface segment parametrised by æ(u, v) = u? cos v, y(u, v) = u² sin v, z(u, v) = u², where 1 < u < 3 and 0 < v < 27.Let S be the surface parametrized by R(u, v) = (2u sin v, 2u cos v, -v), where 0 ≤ u ≤ 2 and 0 ≤ ≤. Evaluate f4yz² do. SFind the surface area of the parametric surface = r(u, v) (u + sin(v), v + sin(u), u-v) where -≤u≤π and T ≤ ≤TT. Enter your answer rounded to 2 decimal places.
- Find the surface area of the surface parametrized by φ(u, v) = (u2 + v, u, v) with 0 ≤ v ≤ 4 and (v/4) ≤ u ≤ 1.Q3A) Find normal line and parallel plane to the function f(x, y, z) = xz siny-√3 At point (1,5,2). 20 rdrdo, cos20 B)Evaluate the integrals: i) f/4 ii) f/2/2finy z² sinx dz dx dy. csiny.Express the area of the surface obtained by rotating the curve y = %In sec(2x) between x = 0 and x = - about the y-axis as %3D %3D an integral. A) 2mx sec(2x) dx. B) 2짜1+am(22d. +tan? (2x)dx. C) n sec(2x) In sec(2x) dx. n 5 In sec(2x)1+-tan2(2x)dx. E) None of the above.
- Let S be the portion of the helicoid parametrized by u COS V g(u, v) = u sin v 0//₁ F. ds, where F(x, y, z) = (-6x³ + 2yz) i + (-6y³ + sin¹ (3xz)) j+ (2z+cos (3x²y²)) k and Sis S the outward-oriented surface of the solid E, which is the right hemisphere bounded by x² + y² + z² = 64 and the plane 2 x = 0. Calculate Enter an exact answer. Provide your answer below: JfF.dS=Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the tangent plane to S at the point (, 1, ).Let Sbe the surface of the sphere of radius 6 centered at the origin, and let F(x, Y, z) = x°zi+ (3yz3 + 2²)j+ (y² + sin z) k. Find F- dS. Select one: а. 18т b. бл O c. O O d. \(24\pi\) O e. \(12\pi\)Find the coordinates of the centroid of the curvex = et cos t, y = et sin t, 0 ≤ t ≤ p.9. Let S be the surface parametrized by (u, v³, u + v) where 0Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,