Theorem Definition and 1000 Threads

Homework Statement Find all the numbers c that satisfy the conclusion of the Mean Value Theorem for the functions f(x)=\dfrac{1}{x-2} on the interval [1, 4] f(x)=\dfrac{1}{x-2} on the interval [3, 6] I don't need help solving for c, I just want to know how I can verify that the hypotheses of...

Homework Statement Can somebody explain to me how the first two steps are performed? The Attempt at a Solution I have no idea how to start the question. I tried using an equation for sin^6 x derived by (cos x + i sinx)^6 = cos 6x+isin 6x but the solution becomes way too hard.

Homework Statement Please see the following,I am confused by the word "only". Homework EquationsThe Attempt at a Solution I understand that the Compatibility theorem ensures we can find a basis of common eigenfunctions of \hat{A} ,\hat{B}.If each pair of eigenvalues {A_i,B_j} identifies...

It says that there is no value of a,b and c, with n>2 and all integer numbers that satisfies this: a^n=b^n+c^n I'm only going to use the cosine theorem. Let's consider three points A, B and C. They form the three sides of a triangle: a, b and c. The sides forms three angles, which can go from...

Background: I am taking an undergraduate fluid mechanics class. I seem to have a misunderstanding with my interpretation of Reynolds Transport theorem (RTT), which I have written below: $$\frac{DB_{sys}}{Dt} = \frac{\partial}{\partial t}\int_{CV}\rho bd V +\int_{CS}\rho b \vec{V}\cdot...

Homework Statement A 2.90 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0360 m . The spring has force constant 860 N/m . The coefficient of kinetic friction between the floor and the block is 0.35 . The block and spring are released from rest...

In your opinion did Fermat have a proof for his theorem?

Homework Statement Verify Stokes' theorem ∫c F • t ds = ∫∫s n ∇ × F dS in each of the following cases: (a) F=i z2 + j y2 C, the square of side 1 lying in the x,z-plane and directed as shown S, the five squares S1, S2, S3, S4, S5 as shown in the figure. (b) F = iy + jz + kx C, the three...

Hello! I looked over a proof of Noether theorem and I am a bit confused about the last step. So they got that ##\delta q(t) p(t)## is constant (I just took the one dimensional case here) where ##\delta q## is a variation of the q coordinate and p is the momentum conjugate of q. I am not sure I...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.7 (Fermat's Little Theorem) ... Theorem 8.7 and its proof read as follows...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.7 (Fermat's Little Theorem) ... Theorem 8.7 and its proof read as follows: My questions regarding...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.6 ... Theorem 8.6 and its proof read as follows: In the above text, Anderson and Feil write the...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.6 ... Theorem 8.6 and its proof read as follows: In the above text, Anderson and Feil write the...

How can I derive that the work of a force perpendicular to velocity is always zero from the theorem of Noether? I have heard that there is a relation between these two but in Google I found nothing. Thank you very much

Homework Statement The sixth term of the expansion of (x-1/5)n is -1287/(3125)x8. Determine n. Homework Equations tk+1=nCkan-kbk The Attempt at a Solution tk+1=nCkan-kbk t5+1=nC5(x)n-5(-1/5)5 This is where I'm stuck. Do I sub in -1287/(3125)x8 to = t6? If so what do I do from here...

Homework Statement 1. Given the binomial (x2-x)13determine the coefficient of the term of degree 17. Answer = -715 2. Given the binomial (2x+3)10 determine the coefficient of the term containing x7. Answer = 414720 2. Homework Equations tk+1=nCkan-kbk The Attempt at a Solution #1 - What...

Whittaker (1st Edition, 1902) P.132, gives two proofs of Fourier's theorem, assuming Dirichlet's conditions. One proof is Dirichlet's proof, which involves directly summing the partial sums, is found in many books. The other proof is an absolutely stunning proof of Fourier's theorem in terms of...

Hi everyone, I use Wick's theorem to decompose expectation values of a string of bosonic creation and annihilation operators evaluated at the vacuum state. This can only be done when the time evolution is driven by a Hamiltonian of the form: H=\sum_{i,j}{\epsilon_{i,j} c^{\dagger}_{i}c_{j}}...

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it. I honestly will never use the higher dimensional version but I still want to see a full proof...

Homework Statement find the number of polynomials f(x) that satisfies the condition: f(x) is monic polynomial, has degree 1000, has integer coefficients, and it can divide f(2x^3 + x) i would very much prefer that you guys give me hints first. thanks Homework Equations remainder factor theorem...

We talked about Fibonacci numbers, and I wondered: Can any natural number be construed by a sum of unique Fibonacci numbers? My guess was yes, and a C program I wrote confirms that to be up to about 2,000, but that's of course is no proof. The best semi-proof I could come up with is that the...

Homework Statement If $$C = 1+cos\theta+...+cos(n-1)\theta,$$ $$S = sin\theta+...+sin(n-1)\theta,$$prove that $$C=\frac{sin\frac{n\theta}{2}}{sin\frac{\theta}{2}} cos\frac{(n-1)\theta}{2} \enspace and \enspace S = \frac{sin\frac{n\theta}{2}}{sin\frac{\theta}{2}}sin\frac{(n-1)\theta}{2}$$...

Hi Guys, at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables...

Homework Statement (y4 - 5y2 + 2y - 15) / (3y - √(2)) The answer says (2√(2)/3)-(1301/81)...

Surface S and 3D space E both satisfy divergence theorem conditions. Function f is scalar with continuous partials. I must prove Double integral of f DS in normal direction = triple integral gradient f times dV Surface S is not defined by a picture nor with an equation. Help me. I don't...

Homework Statement No actual problem, thinking about the telescoping series theorem and Grandi's series For reference Grandi's series S = 1 - 1 + 1 - 1... Homework Equations [/B] The telescoping series theorem in my book states that a telescoping series of the form (b1 - b2) + ... + (bn -...

Hello! (Wave) We say that the space $\Omega$ satisfies the exterior sphere condition at the point $x_0 \in \partial{\Omega}$ if there is a $y \notin \overline{\Omega}$ and a number $R>0$ such that $\overline{\Omega} \cap \overline{B_y(R)}=\{ x_0 \}$. Let the function $\phi \in...

Homework Statement Show that Dx∫f(u)du = f(x) Where the integral is evaluated from a to x. (Hint: Do Taylor expansion of f(u) around x). Homework Equations None The Attempt at a Solution I have ... = Dx(F(u)+C) = Dx(F(x-a)+C) = dxF(x) - dxF(a) = f(x)-f(a). My problem is that it should be...

Homework Statement Prove that $$ \lim_{x\to 0} \sqrt{x^3+x^2}\; \sin\left(\frac{\pi}{x}\right) = 0 $$ using Sandwich theorem Homework Equations Sandwich Theorem The Attempt at a Solution Now we know that sine function takes values between -1 and 1. ## -1 \leqslant...

Hi, this is a newbee question. Does the Fundamental Theorem of Calculus supply a visual (graphical) way of linking a function (F(x)) with its derivative (f(x))? That is, the two-dimensional area under a curve in [a,b] for f(x) is always equals to the one-dimensional distance F(b)-F(a)? If...

Homework Statement In the first and second photo , it's stated earlier that the C is the boundary of surface on xy plane , but in the question in the 3rd picture , it's not stated that the C is on which surface , so , how to do this question ? For ∫F.dr , i am not sure how to get r , coz i am...

Hey guys, I am supposed to solve for voltage and current on R4 using Thevenin's theorem here. Values are following: U = 100V R1 = 310 R2 = 610 R3 = 220 R4 = 570 R5 = 200 Now, I know I need to solve for Rth and Vth, so I put the circuit into simulation and figured out voltage on R3 is equal to...

Hello everyone! I am reviewing the derivation of the Virial Theorem from an introductory Astrophysics book (Carroll and Ostlie's) and found a step I couldn't follow. I've attached a photo of the step. Can anyone explain how Newton's Third Law brings about eqn 2.41? I don't see how that first...

Homework Statement I understand the proof of the implicit function theorem up to the point in which I have included a photo. This portion serves to prove the familiar equation for the implicit solution f(x,y) of F(x,y,z)=c. My confusion arises between equations 8.1-4 and 8.1-5 when it is stated...

Homework Statement i can't find the normal vector here . In my book , outwards vector is . (Refer to photo 1 ) The question is in photo 2 , i am aksed to use stoke's theorem to evalutae line integral of vector filed But , now the problem is i can't express z in terms of y and x . Can anyone...

I learned in Analytical Mechanics: "Emmy Noether's theorem shows that every conserved quantity is due to a symmetry". The examples I learned where conservation of energy as symmetry in time and conservation of momentum as symmetries in space. Now I wonder, do universal constants are also due to...

Homework Statement [/B] ##C_\rho## is a semicircle of radius ##\rho## in the upper-half plane. What is $$\lim_{\rho\rightarrow 0} \int_{C_{\rho}} \frac{e^{iaz}-e^{ibz}}{z^2} \,dz$$Homework Equations If ##C## is a closed loop and ##z_1, z_2 ... z_n## are the singular points inside ##C##...

Consider the lagrangian of the real scalar field given by $$\mathcal L = \frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4$$ Disregarding snail contributions, the only diagram contributing to ## \langle p_4 p_3 | T (\phi(y)^4 \phi(x)^4) | p_1 p_2 \rangle## at...

Homework Statement Consider the beam shown in (Figure 1) . Suppose that a = 15 in. , b = 8 in. , c = 1 in., and d = 4 in. Determine the moment of inertia for the beam's cross-sectional area about the x axis...

Homework Statement Find the solution of the following integral Homework Equations The Attempt at a Solution I applied the above relations getting that Then I was able to factor the function inside the integral getting that From here I should be able to get a solution by simply finding the...

1. Homework Statement i attached the problem statement as an image file Homework Equations p(x) = (x-c)q(x) + r The Attempt at a Solution i've simplified it down to ((x-1)^114) / (2^114)(x+1). is there a practical way to approach this besides long division? wolfram alpha gave an extremely...

I just suppose the Bell's Ansatz for the result of measurement to be $$A (\theta,\lambda) $$ Now the parameter lambda could be anything : -a physical quantity like the polarization angle of the incoming photon -the coordinate of a 'world' - the whole wavefunction. ... In the case of the...

Hello again, everyone. Have a multivariate calculus question this time around. If anyone can point me in the right direction and help me see where WebAssign finds me wrong, it would be greatly appreciated. 1. Homework Statement Homework Equations ∫∫ScurlF ⋅ dS = ∫CF ⋅ dr The Attempt at a...

Homework Statement I am trying to express ##T(\phi(x1)\Phi(x2)\phi(x3)\Phi(x4)\Phi(x5)\Phi(x6))## in terms of the Feynman propagators ##G_F^{\phi}(x-y)## and ##G_F^{\Phi}(x-y)## where ##G_F^{\phi}(x-y) =\int \frac{d^{4}k}{(2\pi)^{4}}e^{ik(x-y)} \frac{ih}{-k.k - m^2 -i\epsilon} ## and...

<Moderator's note: Moved from a technical forum, so homework template missing> Sorry i have one question to ask how to check the v.dl part in this problem i cannot do this problem as it is too hard to integrate the equation How did griffith get this long-horrible equation(see the orange...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Theorem 1.4 ... ... Theorem 1.4 reads as follows: Questions 1(a) and 1(b) In...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Theorem 1.4 ... ... Theorem 1.4 reads as follows: Questions 1(a) and 1(b) In the above...

The thread I wanted to post my question on got closed. Recapitulating: The best (simplest) account I have found to date for the Bell inequality (SPOT stands for Single Photon Orientation Tester): Imagine that each random sequence that comes out of the SPOT detectors is a coded message. When...

1. The problem statement, all variables and given/ You must push a box up an incline plane (the angle being constant : a), to a person waiting to receive it, who is a distance of h(constant) vertically above you. Though the slope is slippery, there is a small amount of friction with kinetic...

I don't know how to start proving this theorem, so can someone please help? I need to prove that the circumcircles all intersect at a point M. Thank you! Miquel's Theorem: If triangleABC is any triangle, and points D, E, F are chosen in the interiors of the sides BC, AC, and AB, respectively...