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Consider the following vector-valued function: y : (−π,0) × (−1,1) → R³, y(u, v) = {cosh (v) cos(u), v, cosh (v) sin(u)}. Sketch the values of y obtained by holding v = Vo constant and varying u, where (i) Vo = ±½¼, (ii) vo = ±½, and (iii) vo = ±³ (you should draw six curves). Sketch the values of y obtained by holding u = uo constant and varying v, −7, and (iii) u。 =— 4 37T U₁ = 7, (ii) u = − == Sketch the full image of y. where (i)

Consider the following vector-valued function: y : (−π,0) × (−1,1) → R³, y(u, v) = {cosh (v) cos(u), v, cosh (v) sin(u)}. Sketch the values of y obtained by holding v = Vo constant and varying u, where (i) Vo = ±½¼, (ii) vo = ±½, and (iii) vo = ±³ (you should draw six curves). Sketch the values of y obtained by holding u = uo constant and varying v, −7, and (iii) u。 =— 4 37T U₁ = 7, (ii) u = − == Sketch the full image of y. where (i)

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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(4) Consider the following vector-valued function: y: (π,0) x (-1, 1) → R³, y(u, v) = {cosh(v) cos(u), v, cosh(v) sin(u)}. (a) Sketch the values of y obtained by holding v = v₁ constant and varying u, where (i) Vo = ±1, (ii) vo = ±½, and (iii) vo = ±³ (you should draw six curves). (b) Sketch the values of y obtained by holding u = u。 constant and varying v, where (i) Uo = (ii) u -7, and (iii) uo 29 π 4' == (c) Sketch the full image of y. = 3πt 4
Transcribed Image Text:(4) Consider the following vector-valued function: y: (π,0) x (-1, 1) → R³, y(u, v) = {cosh(v) cos(u), v, cosh(v) sin(u)}. (a) Sketch the values of y obtained by holding v = v₁ constant and varying u, where (i) Vo = ±1, (ii) vo = ±½, and (iii) vo = ±³ (you should draw six curves). (b) Sketch the values of y obtained by holding u = u。 constant and varying v, where (i) Uo = (ii) u -7, and (iii) uo 29 π 4' == (c) Sketch the full image of y. = 3πt 4
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