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Show that (u, v) = (4u + 6, u − v, 7u + v) parametrizes the plane 2x − y − z = 12. Then: (a) Calculate Tu, Tv, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v) : 0 ≤ u ≤ 7,0 ≤ v ≤ 5. (c) Express f(x, y, z) = yz in terms of u and v and evaluate ſƒ ƒ(x, y, z) dS. (a) Tu = " TV = (b) Area(S) = = (c) ffs f(x, y, z) ds = ‚ n(u, v) = "

Show that (u, v) = (4u + 6, u − v, 7u + v) parametrizes the plane 2x − y − z = 12. Then: (a) Calculate Tu, Tv, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v) : 0 ≤ u ≤ 7,0 ≤ v ≤ 5. (c) Express f(x, y, z) = yz in terms of u and v and evaluate ſƒ ƒ(x, y, z) dS. (a) Tu = " TV = (b) Area(S) = = (c) ffs f(x, y, z) ds = ‚ n(u, v) = "

Advanced Engineering Mathematics
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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Show that (u, v) = (4u + 6, u — v, 7u + v) parametrizes the plane 2x − y — z = 12. Then: (a) Calculate Tỵ, Tv, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 7,0 ≤ v ≤ 5. (c) Express f(x, y, z) = = yz in terms of u and v and evaluate ſ¸ ƒ (x, y, z) dS. (a) Tu (b) Area(S) = (c) ſſ¸ ƒ (x, y, z) dS = = , Tv = ‚ n(u, v) = -0
Transcribed Image Text:Show that (u, v) = (4u + 6, u — v, 7u + v) parametrizes the plane 2x − y — z = 12. Then: (a) Calculate Tỵ, Tv, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 7,0 ≤ v ≤ 5. (c) Express f(x, y, z) = = yz in terms of u and v and evaluate ſ¸ ƒ (x, y, z) dS. (a) Tu (b) Area(S) = (c) ſſ¸ ƒ (x, y, z) dS = = , Tv = ‚ n(u, v) = -0
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