Show that R(u, v) = (5u + 2, u – v, 9u + v) parametrizes the plane 2x -y-z = 4. Then: (a) Calculate eu, e, and Ñ(u, v). (b) Find the area of S = R(D), where D = (u, v): 0 ≤u ≤ 7,0 ≤ v ≤ 5. (c) Express f(x, y, z) = yz in terms of u and u and evaluate [[ f(x, y, z) dS. v (a) eu = , ev ‚ Ñ(u, v) = = (b) Area(S) = (c) [[¸ ƒ(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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Show that R(u, v) = (5u + 2, u − v, 9u + v) parametrizes the plane 2x − y − z = 4. Then:
(a) Calculate eu, ev, and Ñ(u, v).
(b) Find the area of S = R(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
[[ f(x, y, z) ds.
(a) eu =
, ev =
(b) Area(S) =
(c) ff f(x, y, z) ds =
=
‚ Ñ(u, v) =
Transcribed Image Text:Show that R(u, v) = (5u + 2, u − v, 9u + v) parametrizes the plane 2x − y − z = 4. Then: (a) Calculate eu, ev, and Ñ(u, v). (b) Find the area of S = R(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 [[ f(x, y, z) ds. (a) eu = , ev = (b) Area(S) = (c) ff f(x, y, z) ds = = ‚ Ñ(u, v) =
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