Asap plz handwritten solution acceptable (1 point) Suppose that surface o is parameterized by1#r(u, v) = (u cos(4v), u sin(4v), v), 0≤ u≤7 and 0 ≤ v≤ ¹and f(x, y, z)= x² + y² + z². Set up the surface integral (you don't need to evaluate it).[[ f(x, y, z) ds = [[ f(x(u, v), y(u, v), z(u, v))R=pi/2070u^2 + y^2Ər ƏrXdvdAsqrt(1+16u^2)du dv

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Answered: [ f(x, y, z) ds = 2) ds = f f f (x(u,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane at (2, 5, 1) in terms of (u, v) as well as in terms of (x, y, z).
Find an equation of the tangent plane to the given surface
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3. A donut with major radius R and minor radius r can be represented parametrically by r(u, v) = ((R+r cos u) cos v, (R+r cos u) sin v, r sin u) for 0 ≤ u ≤ 27 and 0 ≤ v ≤ 2π. What is the surface area of the donut?
Let z = g(r, y) = f(3 cos(ry), y + e") provided that f(3, 5) = 7, fi(3, 5) = 2, f2(3, 5) = 5. i) Find g, (0, 4). i) Find 92 (0, 4). iii) Find the equation of the tangent plane to the surface z = f(3 cos(ry), y + ev) at the point (0, 4). Türkçe: f(3, 5) = 7, fi(3,5) = 2, f2(3, 5) = 5 olmak üzere z = g(x, y) = f(3 cos(zy), y + e") olsun. i) 91 (0, 4) değerini bulunuz. in 92 (0, 4) değerini bulunuz. im) z = f(3 cos(ry), y + e*") yüzeyine (0, 4) noktasında teğet düzlemin denklemini bulunuz. O i) 20, ii) 5, ii 20x + 5y - z = 13 O i) 20, i) 5, ii) 20x - 5y - z = -1 O i) 20, i) 15, ii) 20x + 15y + z = 53 O i) 60, i) 5, ii) 60x - 5y - z = -47 O ) -40, i) 15, ii) -40x + 15y + z = -27
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[ f(x, y, z) ds = 2) ds = f f f (x(u, v), y(u, v), z(u, v)) || R Ər ἂν dA