Assume that now | X = R. Show that x.x=0 [Hint: Differentiate constion't ev]. Deduce that I is a constant along solution of system. [ Diffrentrate Previous eq. again].
Assume that now | X = R. Show that x.x=0 [Hint: Differentiate constion't ev]. Deduce that I is a constant along solution of system. [ Diffrentrate Previous eq. again].
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![Date:
/20
Day
A
constrained extremisation Problem is expressed
as longronge-multiplier problem with objective
functional
I [x+x] = [[√√₂² ² + y² + 3 ² _k (t) (x² + y² +3²_R²³)]d²
where x = da etc. and integeral has appropriate
fixed limitat
with fixed values of X₂ Y and
Z at the endpoints.
a). Explain what geometric problem is solved here and
local or
global constraint.
for Variable x
As there
b)- show that ewler-longronge eq.
takes the form,
d
d
at
(7) = -ax
Also find Euler - Longronze ey's for y and 3
land write them in vector notation for vector
X = (x, y, z). Give Jemeterical interpretation chat
they tell you.
C). show that Beltrami-identity does not help you.
to solve the equation-
d). Let u be an arbitrary increasing fn of t. show
that
ƒ [√xx²)³+ (y^)³+ (3³) ³ ]du= [[] x² + y + 3³ ] du
where. x'=dx, Explain what this
du
signifies
geometrically and why this means that one can
assumes without loss of generality, that
11 = R along solution of the
Euler-long range equations -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5fb4c48-e210-4c5e-a541-160a60a9de22%2F36e92e63-b5a9-4e78-bb6b-1d4b9b295798%2F7wxoy48_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Date:
/20
Day
A
constrained extremisation Problem is expressed
as longronge-multiplier problem with objective
functional
I [x+x] = [[√√₂² ² + y² + 3 ² _k (t) (x² + y² +3²_R²³)]d²
where x = da etc. and integeral has appropriate
fixed limitat
with fixed values of X₂ Y and
Z at the endpoints.
a). Explain what geometric problem is solved here and
local or
global constraint.
for Variable x
As there
b)- show that ewler-longronge eq.
takes the form,
d
d
at
(7) = -ax
Also find Euler - Longronze ey's for y and 3
land write them in vector notation for vector
X = (x, y, z). Give Jemeterical interpretation chat
they tell you.
C). show that Beltrami-identity does not help you.
to solve the equation-
d). Let u be an arbitrary increasing fn of t. show
that
ƒ [√xx²)³+ (y^)³+ (3³) ³ ]du= [[] x² + y + 3³ ] du
where. x'=dx, Explain what this
du
signifies
geometrically and why this means that one can
assumes without loss of generality, that
11 = R along solution of the
Euler-long range equations -
![e) - Assume that now x1 = R. Show that x-x=0 [Hint:
Differentiate Constion't ev]. Deduce that I is a
constant along solution of system -[ Diffrentrate
Previous eq. again].
f). Find general solution which starts at (x₂ 4₂3) = (R₂0₂0)
at t=0.
(Hint: Use that a csat+ basinat +ccostsint = ra
for all values of t only if α²=b²=8² and C=O)
Describe this solution looks like geometrically and
draw a sketch of it. Give on interpretation of
value of Lonzoange multiples L..](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5fb4c48-e210-4c5e-a541-160a60a9de22%2F36e92e63-b5a9-4e78-bb6b-1d4b9b295798%2Fl25cqwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:e) - Assume that now x1 = R. Show that x-x=0 [Hint:
Differentiate Constion't ev]. Deduce that I is a
constant along solution of system -[ Diffrentrate
Previous eq. again].
f). Find general solution which starts at (x₂ 4₂3) = (R₂0₂0)
at t=0.
(Hint: Use that a csat+ basinat +ccostsint = ra
for all values of t only if α²=b²=8² and C=O)
Describe this solution looks like geometrically and
draw a sketch of it. Give on interpretation of
value of Lonzoange multiples L..
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