Show that (u, v) = (6u + 6, u – v, 1lu + v) parametrizes the plane 2x – y – z = 12. Then: (a) Calculate Tu , T, and n(u, v). (b) Find the area of S = ¢(D), where D = (u, v) : 0 < u < 4,0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that (u, v) = (6u + 6, u – v, 11u + v) parametrizes the plane 2x – y – z = 12. Then:
(a) Calculate Tu , Ty, and n(u, v).
(b) Find the area of S = D(D), where D = (u, v) : 0 < u < 4,0 < v< 4.
(c) Express f(r, y, z) = yz in terms of u and v and evaluate ls f(x, y, z) dS.
n(u, v) =
Tv
(a) Tµ
(b) Area(S)
(c) fs f(x, y, z) dS =
Transcribed Image Text:Show that (u, v) = (6u + 6, u – v, 11u + v) parametrizes the plane 2x – y – z = 12. Then: (a) Calculate Tu , Ty, and n(u, v). (b) Find the area of S = D(D), where D = (u, v) : 0 < u < 4,0 < v< 4. (c) Express f(r, y, z) = yz in terms of u and v and evaluate ls f(x, y, z) dS. n(u, v) = Tv (a) Tµ (b) Area(S) (c) fs f(x, y, z) dS =
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