Show that Þ(u, v) = (2u + 6, u — v, 3u + v) parametrizes the plane 2x - y - z = 12. Then: (a) Calculate Tu, T₁, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 9,0 ≤ v ≤7. (c) Express f(x, y, z) = yz in terms of u and v and evaluate ſ¸ ƒ(x, y, z) dS. (a) Tu , Tv = ‚ n(u, v) = = " = (b) Area(S) = (c) [ f(x, y, z) ds =
Show that Þ(u, v) = (2u + 6, u — v, 3u + v) parametrizes the plane 2x - y - z = 12. Then: (a) Calculate Tu, T₁, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 9,0 ≤ v ≤7. (c) Express f(x, y, z) = yz in terms of u and v and evaluate ſ¸ ƒ(x, y, z) dS. (a) Tu , Tv = ‚ n(u, v) = = " = (b) Area(S) = (c) [ f(x, y, z) ds =
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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Transcribed Image Text:Show that Þ(u, v) = (2u + 6, u − v, 3u + 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 ≤ 9,0 ≤0 ≤7.
(c) Express f(x, y, z) = yz in terms of u and u and evaluate f f (x, y, z) dS.
(a) Tu =
=
(b) Area(S) =
(c) [ f(x, y, z) ds =
, T
=
‚ n(u, v) =
"
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