Lagrange Definition and 541 Threads

Hi everyone. This is my first post here and I was wondering if any of you could help me. The question is to prove that 1 + \frac{x}{3} - \frac{x^2}{9} < (1 + x)^\frac{1}{3} < 1 + \frac{x}{3} if x>0. The question is in a section on the lagrange remainder theorem. The fact that the first...

Does the Klein-Gordon Lagrange density maximize or minimise the solution of the Klein-Gordon equation?

I know this is supposed to go in the HW forum but its not working there so I'm trying it here, and I'm actually running into the same problem with another problem AGAIN. Someone tell me if I am doing this right: --- \nablaHomework Statement Find the extrema of f(x,y)=x-y ; subject to...

Homework Statement Use lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x,y) = x+3y, x2+y2≤2 Homework Equations grad f = λ grad g The Attempt at a Solution to find critical points in the interior region...

How to solve this problem? : Consider two particles of masses m1 and m2. Let m1 be confined to move on a circle of radius a in the z = 0 plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius b in the z = c plane, centered at x = v = 0. A light (massless) spring of...

Homework Statement A particle of mass, m1, is constrained to move in a circle with radius a at z=0 and another particle of mass, m2, moves in a circle of radius b at z=c. For this we wish to write up the Lagrangian introucing the constraints by lagrange multipliers and solve the following...

Lagrange mult. ---finding max Homework Statement [/b] probability mass function is given by p(x1,...,xk; n, p1,... pk) := log (n!/x1!...xk!) p1^x1 p2^xk Here, n is a fixed strictly positive integer, xi E Z+ for 1 < i < k, \Sigma xi=n, 0 <pi <1, and \Sigma pi=1 The maximum...

Homework Statement Prove a \times (b \times c) = (a * c)b - (a*b)c For orthagonal coordinates, a,b,c Homework Equations Cross Product and Dot Product The Attempt at a Solution I thought about expanding both sides out and proving they are equal, but I just realized that the...

I'm trying to follow the idea behind Lagrange multipliers as given in the following wikipedia link. http://en.wikipedia.org/wiki/Lagrange_multipliers I follow the article right up until the point where it goes: 'To incorporate these conditions into one equation, we introduce an...

Homework Statement Using the method of lagrange multipliers, find the points on the curve 3x² - 4xy + 6y² = 140 which are closest and furthermost from the ORIGIN and the corresponding distances between them The Attempt at a Solution I have done roughly half the question but appear to be...

can anybody please clearly explain me the difference between these two frames of reference with few examples. my exames are closing up. please help me.

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

find min/max: f(x,y)=xy with constraint being 4x^2+9y^2=32 [gradient]f=[lambda]gradient g The Attempt at a Solution I thought I understood the Lagrange problems, but I can't seem to get the minimum right on the last few problems. I get x=+/-2 and then plug back into find y, then I use my...

I have used this method quite a lot but I have never completely understood the proof. The only book I have that provides a proof is Shifrin's "Multivariable Mathematics" which I find kind of confusing. Stewart's "proof" is more or less just geometric intuition. Does anyone know of a book that...

Homework Statement i needed to find the max and min possible volume for a box with edges that = 200cm and surface area that = 1500cm^2 using Lagrange multipliers.Homework Equations edges: 4x + 4y + 4z = 200cm Area: 2xy + 2xz + 2yz = 1500 cm^2 Volume = xyzThe Attempt at a Solution i brought it...

Hello everyone! I'm trying to find the relation between the lagrangian density and the hamiltonian, does anyone know how they are related? I also need a reference where I can find the relation. Thanks!

Hello: Problem1: The temp of the circular plate D= {(x1,x2) | x1^{2} + x2^{2} \leq 1} is given by T=2x^{2} -3y^{2} - 2x. Find hottest and coldest points of the plate. Problem 2 Show that for all (x1,x2,x3) \in R^{3} with x1>0, x2>0, x3>0 and x1x2x3 = 1, we have x1+x2+x3 \geq3...

Hi, Why is -BEi used instead of +BEi as the lagrange multiplier for indistinguishable particles? How is it justified? I've been reading a book about statistical mechanics and it introduces lagrange multipliers first for distinguishable particles- it has ln(ni) + a + BEi = 0. (where a is...

hi everyone! I'm having difficulty figuring this problem out. so here goes: f(x) = sin(x) Use the Lagrange formula to find the smallest value of n so that the nth degree Taylor polynomial for f centered at x = 0 approximates f at x = 1 with an error of no more that 0.001. whatever help...

We're suppose to minimize f(x,y,z)=x^2+y^2+z^2 subject to 2x+y+2z=9. I only ever remember learning how to do f(x,y) would it be the same equation? Thus, f(x,y,\lambda) = f(x,y) + \lambda g(x,y)? Meaning f(x,y,z,\lambda) = x^2+y^2+z^2 + \lambda (2x+y+2z-9) and then continue solving for each...

http://www.geocities.com/asdfasdf23135/advcal29.JPG I am wondering whether the above statement is true. "A necessary condition for the constrained optimization problem to have a GLOBAL min or max is that..." Should the word local replace global? I am confused about the method of...

hi all , i am new at this forum , so i don't exactly know the rules about the topics and their sorting i am self studying lagrange dynamics. so my question is : when writing lagrange equations for aparticle ,& the particle is in conformity with the constraints...

http://img151.imageshack.us/img151/5562/updatequicklyte1.jpg how would i solve it using MATLAB ? I tried many times but i didnt get the same answer may anyone help me please ?

I am a physics student just finishing my sophomore year, and i was looking into what i could expect in upcoming intermediate mechanics. I noticed that Lagrange mechanics seems to be a big topic, and that i need to understand it to move forward in my studies. Being too impatient to wait for the...

(1) f(x,y,z)=x+2y (2) x+y+z=1 (3) y^2+z^2=4 1=\lambda 2=\lambda+2y\mu 0=\lambda+2z\mu u=\frac{1}{2y} y=\pm\sqrt2 \ \ \ z=\pm\sqrt2 Plugging into equation 2 to solve for x. How do I know to use either y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2 ... similarly with my values for z. edit: NVM, I'm an...

Homework Statement A uniform chain of length L and mass M is constrained to move in a frictionless tube. Initially a fraction (1-f0) of the chain rests in a horizontal section of the tube. The remaining fraction f rests in a section of the tube that is inclined downward from the horizontal at...

I'm trying to follow a professor's notes for finding Christoffel symbols for a two-sphere. He gives the following two equations: The Lagrangian for a two sphere:L = \left( \frac{d\theta}{ds} \right)^2 + sin^2\theta \left( \frac{d\phi}{ds} \right)^2 The Euler Lagrange equation: \frac{d}{ds}...

http://img100.imageshack.us/img100/9016/linalggp1.jpg for (a): does that mean i must compute l0(t), l1(t) and l2(t), and i wasn't sure how to do this with the lagrange polynomial formula given, so i found one online and did it, I'm not sure if this is correct, but my l0(t) looks like this: =...

[SOLVED] Euler Lagrange Equation Hi there , I am missing a crucial point on the proof of Euler Lagrange equation , here is my question : \frac{\partial f}{\partial y}-\frac{d}{dx}\left(\frac{df}{dy^{'}}\right)=0 (Euler-Lagrange equation) If the function "f" doesn't depend on x explicitly...

Homework Statement The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood. They want me to find the length, width, and height...

I'm having a little trouble with another old test question. It states: Use LaGrange multipliers to find the point on the line 2x + 3y = 3 that is closest to the point P(4, 2). I assume that my constraint is g(x, y) = 2x + 3y = 3, and I have to come up with a function f(x, y) to be...

Hi Everyone, I want to use the Lagrange approach (which I am not terribly familiar with) to model a system with friction. I was thinking of modeling the losses due to friction as a simple constant dissipation of energy over time. Can I simply add a term of the form -Ft to the potential...

Homework Statement A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. The only external force is that of gravity. If the smaller cylinder starts rolling from rest on top of the bigger cylinder , use the method of lagrange multipliers to find the point...

Homework Statement A particle moves on the surface of a sphere. Write down the Lagrange equations.Homework Equations The Attempt at a Solution So since it is a free particle, there is no V in the Lagrangian, correct? So L = T and I can write: L = 1/2 m (R^2 \cos^2 \phi \dot{ \theta}^2 + R^2...

Lagrange equation of motion (from Marion 7-7) A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find...

Hi! I've been studying Dirac's programme for some time and I realized that there's something missing: Actually this is missing in every standard book on classical mechanics concerning how constraints are implemented in the lagrangian. They are usually inserted with some unknown variables...

hi, i just learned about lagrange multipliers and i am very confused about how to derive and use them. another thing, how would you use them to find points on a surface that are closest to a given point outside the surface

Homework Statement find the max and min of f(x,y)=x^2y, constraint x^2+y^2=1 Homework Equations None. The Attempt at a Solution I found that possible points use the procedure of the method of lagrange multiplier, I got (\pm\sqrt{2/3}, \pm\sqrt{1/3} so 4 points total. But do I have to...

Hello, I was hoping someone would be able to clarify a problem I've got. A lagrange multiplier can be introduced into an action to impose a constraint right? I was wondering what relation lagrange multipliers have to gauge conditions, which are imposed by hand. Am I correct in saying that...

Homework Statement Find the maximum x1, x2, x3, in the ellipsoid x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained.Homework Equations The Attempt at a Solution My teacher said to use the lagrange multiplier. So far, I have that we are maximizing x1, x2, and x3...

There's a homework problem that I've been struggling over: Find a formula for the truncation error if we use 1 + x^2 + x^4 +x^6 to approximate 1/(1-x^2) over the interval (-1, 1). Now, I assume that you need to use LaGrange error but I'm not sure how to proceed. Any help would be greatly...

Question: Use Lagrange multiplier method to determine the point on the curve y=1-x^2 that maximises the function f(x,y)=2x + y. Hence find the maximum value of f. Attempt at Solution: Okay I used the Lagrange method to get a point on the curve and I got (1,0) How do I find the...

Consider the function f(t) = ln (1 +2x) Give a formula for f^(n) (x) [**the nth derivative] valid for all n >= 1 and find an upper bound for | f^(n) (x) | on the interval -0.25 <= x <= 0.25. [ the error ]. I found the nth derivative to be f^(n) (x) = (-1)^n+1 * 2^n /n * n...

When we seek the extreaml value of the functional \Phi(\gamma) = \int_{t_0}^{t_1} L(x(t),\dot{x}(t),t)dt where x can be taken from the entire E^n then we come to the well-known Lagrange equations. Now when we are given a constraint, that x \in M, where M is a differentiable manifold and when...

I've just started multi dimensional calculus, among which Langrange's Multipliers. I have some questions which will help me grasp the concepts since I'm a very curious guy... a) What are you finding exactly with this technique? b) What is the constraint? c) What does the extra variable...

My math is a little rusty and I want someone to identify the category of problem (Lagrange Multipliers, Simplex method, ...) I have, so that I can read up on the topic and familiarize myself with the technique. To make the problem simple, let's say I have some number of chips of varying...

Hey, I need help with a problem involving Lagrange multipliers... Here is the question: Find the absolute maximum and minimum of the function f(x,y) = x^2-y^2 subject to the constraint x^2+y^2=289. As usual, ignore unneeded answer blanks, and list points in lexicographic order. I...

Hi, how do I interpret the last sum: http://planetmath.org/encyclopedia/LagrangesIdentity.html Sum (...) 1<=k < j <= n Is it the double sum: Sum( Sum( (a_k*b_j - a_j*b_k)^2 from k = 1 to n) from j = 2 to n ) ?

Hello everyone Here is my problem lagrange interpolation polynomial across the points(x0,y0),(x1,y1) and (x2,y2) is given by y0L0(x) + y1L1(x) + y2L2(x) where L0(x)=-x and L1(x)=x ^2 + x Therefore L2(x) is given by I tried it but i could'nt crack it

Hi, Does anyone know how to design a 8x lagrange interpolation filter in matlab? From what I understand, let say my input is input = [1 2 3 4 3 2 1] let say if I want to interpolate by 2, then I insert 0 between every sample. input_pad = [1 0 2 0 3 0 4 0 5 0 4 0 3 0 2 0 1] then...