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Show that (u, v) = (5u+5, uv, 9u + v) parametrizes the plane 2x - y -z = 10. Then: (a) Calculate T₁, T , and n(u, v). V₁ (b) Find the area of S = Þ(D), where D = (u, v) : 0 ≤ u ≤ 3,0 ≤ v≤7. (c) Express f(x, y, z) = yz in terms of u and u and evaluate ff f(x, y, z) dS. T (a) Tu = <5,1,9> (b) Area(S) = 105sqrt(6) (c) ffç f(x, y, z) ds = <0,-1,1> , n(u, v) = <10,-5,-5>

Show that (u, v) = (5u+5, uv, 9u + v) parametrizes the plane 2x - y -z = 10. Then: (a) Calculate T₁, T , and n(u, v). V₁ (b) Find the area of S = Þ(D), where D = (u, v) : 0 ≤ u ≤ 3,0 ≤ v≤7. (c) Express f(x, y, z) = yz in terms of u and u and evaluate ff f(x, y, z) dS. T (a) Tu = <5,1,9> (b) Area(S) = 105sqrt(6) (c) ffç f(x, y, z) ds = <0,-1,1> , n(u, v) = <10,-5,-5>

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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P.S. the answer for the final question is not 658*105(6)1/2

Show that Þ(u, v) = (5u+5, uv, 9u + v) parametrizes the plane 2x - y - z = 10. Then: (a) Calculate Tu T v, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 3,0 ≤ v≤7. (c) Express f (x, y, z) = yz in terms of u and u and evaluate ff f(x, y, z) dS. (a) T₁ = <5,1,9> T₁ = ,n(u, v) (b) Area(S) = 105sqrt(6) (c) ff f(x, y, z) ds = <0,-1,1> <10,-5,-5>
Transcribed Image Text:Show that Þ(u, v) = (5u+5, uv, 9u + v) parametrizes the plane 2x - y - z = 10. Then: (a) Calculate Tu T v, and n(u, v). (b) Find the area of S = Þ(D), where D = (u, v): 0 ≤ u ≤ 3,0 ≤ v≤7. (c) Express f (x, y, z) = yz in terms of u and u and evaluate ff f(x, y, z) dS. (a) T₁ = <5,1,9> T₁ = ,n(u, v) (b) Area(S) = 105sqrt(6) (c) ff f(x, y, z) ds = <0,-1,1> <10,-5,-5>
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