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y be a real constant with y² 1 for the parametric functional S[x, y)] = ['ª dt [√લ + 2y àý + y² – X(xÿ−ày)], λ>0, – with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. ds dx dy +7 = ds dx = 2(cy) and y ds 33 dy = 2(d+λx), where c and d are constants and

y be a real constant with y² 1 for the parametric functional S[x, y)] = ['ª dt [√લ + 2y àý + y² – X(xÿ−ày)], λ>0, – with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. ds dx dy +7 = ds dx = 2(cy) and y ds 33 dy = 2(d+λx), where c and d are constants and

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Show that the stationary paths of this parametric functional.
y be a real constant with y² 1 for the parametric functional S[x, 3] = [ª dt [√ä² + 2y àÿ + ÿj² – A(xÿ — ày)], - - > > 0, with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. dx ds dy +7 = ds dx dy = 2(c->y) and y + = ds ds 2(d+λx), where c and d are constants and s(t) = √¸² dt √ž² + 2y àÿ + ÿj².
Transcribed Image Text:y be a real constant with y² 1 for the parametric functional S[x, 3] = [ª dt [√ä² + 2y àÿ + ÿj² – A(xÿ — ày)], - - > > 0, with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. dx ds dy +7 = ds dx dy = 2(c->y) and y + = ds ds 2(d+λx), where c and d are constants and s(t) = √¸² dt √ž² + 2y àÿ + ÿj².
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