dx dy dx +γ = 2(c-Ay) and Y. + ds ds ds where c and d are constants and rt 8(t) = √6° Show that dt√x²+2yxy + y². 33 = = 2(d+λx), dx dy + 2 dx +27 ds ds ds dy ds 2 = = 1. 3

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 25E
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y be a real constant with y² + 1 for the parametric functional
1
S[x, y] = {* dt [√ಠ+ 2y àÿ + ÿj² – A(xÿj
√x² + 2y ±ý + ÿ² − \(xÿ − y)], λ>0,
-
with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
ds
dx dy
+7 = = 2(c- Ay) and
ds
where c and d are constants and
t
s(t) = [* dt √ã² .
dt√√√x² + 2y xy + y².
dx dy
γ + = 2(d+\x),
ds ds
Show that
2
dx
ds
+27
dx dy
ds ds
2
+
རྩེ་|
dy
= 1.
3
ds
Transcribed Image Text:y be a real constant with y² + 1 for the parametric functional 1 S[x, y] = {* dt [√ಠ+ 2y àÿ + ÿj² – A(xÿj √x² + 2y ±ý + ÿ² − \(xÿ − y)], λ>0, - with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. ds dx dy +7 = = 2(c- Ay) and ds where c and d are constants and t s(t) = [* dt √ã² . dt√√√x² + 2y xy + y². dx dy γ + = 2(d+\x), ds ds Show that 2 dx ds +27 dx dy ds ds 2 + རྩེ་| dy = 1. 3 ds
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,