What is Infinite: Definition and 1000 Discussions

when using the reimann integral over infinite sums, when is it justifiable to interchange the integral and the sum? \int\displaystyle\sum_{i=1}^{\infty} f_i(x)dx=\displaystyle\sum_{i=1}^{\infty} \int f_i(x)dx thanks ahead for the help!

Homework Statement Two parallel plates having charges of equal magnitude but opposite sign are separated by 14.0 cm. Each plate has a surface charge density of 37.0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates...

I'm working on a research project and was wondering what you could use to experimentally create a periodic infinite square well (dirac comb?) in a direction orthogonal to a different potential, say a periodic potential. To help you understand what I'm trying to do picture a grid of atoms and...

Gauss' Law problem! Help please! infinite sheet with charge density? In the figure below, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m2. A z-axis, with its origin at the hole's...

Homework Statement Problem: Determine an expression for the magnitude of the magnetic force on a charged particle moving near an infinitely long wire, carrying a current i. Particle with charge q Magnitude of the particles velocity = |v| Magnetic field strength = B Current = i Homework...

Homework Statement Hi all, I am struggling with getting an intuitive understanding of linear normed spaces, particularly of the infinite variety. In turn, I then am having trouble with compactness. To try and get specific I have two questions. Question 1 In a linear normed vector space, is...

Consider the product $$\displaystyle\prod_{n=1}^{+\infty}(1-e^{-2\pi n}e^{2\pi iz})$$ I've proven that this product converges uniformly on compact subsets of complex plane since the serie $\sum_{n=0}^{+\infty}|\frac{e^{2\pi iz}}{e^{2\pi n}}|$ does. Now I'm interested to zeros of $F$, the...

Hello, I found an approximation for this log function: log \Bigg(\frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \Bigg), where \Lambda \rightarrow \infty . The above is approximated to the following, -log \bigg(\frac{\rho}{\rho_o} \bigg) + log \bigg(\frac{2 \Lambda}{\rho_o}...

Homework Statement Twelve infinite long wires of uniform linear charge density (λ) are passing along the twelve edges of a cube. Find electric flux through any face of cube. (see attachment)Homework Equations The Attempt at a Solution I have actually solved the problem but I think there's a...

Homework Statement A large, flat, horizontal sheet of charge has a charge per unit area of 3.15 µC/m2. Find the electric field just above the middle of the sheet.Homework Equations dq = \sigma dA \oint \vec{E} \cdot d\vec{A} = \frac{q_enc}{\epsilon_0} \epsilon_0 = \frac{1}{4 \pi k_e} The...

ello everybody, how can I calculate the group velocity of a wave package in an infinite square well? I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment. But in the well, there are only discrete...

Hi, True or False: Every infinite sequence of natural numbers, who's terms are randomly ordered, must contain every possible subsequence of any length, including infinity. For example, does the infinite and random sequence \small M of natural numbers require that the subsequence {59,1,6}...

energy due to a charge is infinite?? hello.. My professor said "Law of conservation of energy is not applicable to waves." This puzzled me a lot and trying to think otherwise i have a doubt regarding energy due to electric field. It seems that if energy due to electric field and magnetic...

Homework Statement Hi all, I have this problem that was on a recent exam but I did not know how to make sense of it. So, suppose you have three infinite sheets, each layered on top of each other each separated by a distance d. So the first is d above the second, and the second is d above...

Homework Statement Assume a potential of the form V(x)=V_{0}sin({\frac{\pi x}{L}}) with 0<x<L and V(x)=\infty outside this range. Assume \psi = \sum a_{j} \phi_{j}(x), where \phi_{j}(x) are solutions for the infinite square well. Construct the ground state wavefunction using at least 10...

Homework Statement An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity σ1 = 0.3 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.33 μC/m2 is located at x = c = 21.0 cm.. An uncharged infinite conducting slab is placed...

Homework Statement An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity σ1 = 0.57 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.39 μC/m2 is located at x = c = 28.0 cm.. An uncharged infinite conducting slab is placed...

Homework Statement Find the radius of convergence and interval of convergence for the following infinite series \sum_{n=1}^{\∞} \frac{x^n n^2}{3 \cdot 6 \cdot 9 \cdot ... (3n)} Homework Equations Ratio test The Attempt at a Solution Using ratio test we get im not sure how to...

Homework Statement A car is moving with a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90° turn by side of the wall . A fly flying at a constant speed of 100 km/h , start from the wall towards the car at an instant when the car...

In one dimensional problem of infinite square potential well wave function is ##\phi_n(x)=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}## and energy is ##E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}##. Questions: What condition implies that motion is one dimensional. Did wave function describes motion of...

Homework Statement How many terms of the series do we need to add in order to find the sum to the indicated accuracy? Ʃ((-1)n)/(n(10n)) from n=1 to infinity |error| <.0001 I keep ending up with n=log(4)-log(n)

Homework Statement Find the geodesics on a cone of infinite height, x^{2}+y^{2} = \tan{\alpha}^{2}z^{2} using polar coordinates (x,y,z)=(r\cos{\psi},r\sin{\psi},z) with z=r\tan(\alpha) The Attempt at a Solution I am not sure with how should I expres the element dz^{2} ? When it is a...

Homework Statement Show that the infinite series \sum_{n=0}^{\infty} (\sqrt{n^a+1}-\sqrt{n^a}) Converges for a>2 and diverges for x =2The Attempt at a SolutionI'm reviewing series, which I studied a certain time ago and picking some questions at random, I can't solve this one. I tried every...

Homework Statement Find the magnetic field from an infinite slab with constant current density, Jo, in the x direction. ρ(z) = ρ1 x_hat for -b<z<b ρ(z) = 0 for |z| >= b Homework Equations Ampere's Law. The Attempt at a Solution I draw a rectangular prism inside the slab with...

Homework Statement How do you find the electric fields of regions between parallel infinite sheets of charge? The set up: 3 parallel infinite sheets of charge a,b,c from left to right. Region 1 is to the left sheet a. Region 2 is between sheets a and b. Region 3 is between sheets b and c...

Homework Statement Let F be an infinite field (that is, a field with an infinite number of elements) and let V be a nontrivial vector space over F. Prove that V contains infinitely many vectors. Homework Equations The axioms for fields and vector spaces. The Attempt at a Solution...

Hi There, This is my first post in Math, and I can't read a formula beyond arithmetic, so please bear with me. I've always been curious about infinity and how it affects probability. I was reading on Wikipedia about the Infinite Monkey Theorem, and understand (I think) that with a finite...

Hi everybody, while doing a complex analysis exercise, i came to a strange inequality which i don't know how to interpretate. Suppose you have a sequence $\{a_j\}$ of positive real number. Let $\rho$ a positive real number. The inequality i found after some calculation is...

Homework Statement cot^-1 3 + cot^-1 7 + cot^-1 13+... Homework Equations The Attempt at a Solution I first tried to write the nth term of the series t_n = cot^{-1}\left( 2^n + (2n-1) \right) Then I tried to calculate the limit as n→∞. But I simply can't do that. I mean I...

Homework Statement Call a set X Dedekind infinite if there is a 1-to-1 mapping of X onto its proper subset. Prove that every countable set is Dedekind infinite. The Attempt at a Solution I want to say that every countable set can be well ordered. I guess I could just pick some...

Homework Statement Let X be a set and let f be a one-to-one mapping of X into itself such that f[X] \subset X Then X is infinite. The Attempt at a Solution Let's assume for the sake of contradiction that X is finite and there is an f such that it maps all of the elements of X to a...

Hi. I am supposed to explain using phasor diagram how change in excitation current affects power factor and active power of the generator. I have a few different values for excitation current, real power and power factor. Basically, increasing excitation current causes decrease in power factor...

Hello, I heard a scientist on the radio claiming that, if the universe is infinite, that all possible combinations of matter/energy exist somewhere in that infinite-ness. So, for example, as I sit typing, I am wearing a gray sweater. As I understand it, somewhere in the infinite universe I...

I've seen a lot of programs about M Theory and string theory and such which suggest that there could be an infinite number of infinite universes in this multiverse. And according to microwave background radiation our universe is infinite. But how could there be an infinite amount of infinite...

Hi all, I'm trying to integrate the function below with respect to x exp(ix)-exp(-ix) With infinity and negative infinity as the limits. Would the integration be possible?

Happy new year. All the best. I have one question. Is it true? \sum^{\infty}_{k=0}a_kx^k=\sum^n_{k=0}a_{n-k}x^{n-k} I saw in one book relation \sum^{\infty}_{k=0}\frac{(2k)!}{2^{2k}(k!)^2}(2xt-t^2)^k=\sum^{n}_{k=0}\frac{(2(n-k))!}{2^{2(n-k)}((n-k)!)^2}(2xt-t^2)^{n-k} Can you give me some...

Homework Statement I worked out until the last part of the question and 3 equations with 3 unknowns got reduced to this: x - 2y + 3z = 1 x + 3z = 3 The Attempt at a Solution y = 1, x = 3 -3z Letting x = λ where λ is any real number, (x,y,z) = (3,1,0) + λ(-3,0,1)...

Hi, Merry Christmas everyone! If universe is infinite doesn't that violate the second thermodynamics? Because that means there would infinite amounts of matter and/or energy in the universe? Even if all the stars would come to end up like neutron stars white dwarfs or black holes which...

Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression: V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1. (Note that: \pm is plus (+) or minus (-) sign). Could it be referred to as the infinite...

Ok...this must sound stupid, because i didn't found answer on the web and on my books...but i am having trouble with the infinite square well. I want to calculate <x>. V(x)=0 for 0<=x<=a <x>=\frac{2}{a}\int^{a}_{0} x \sin^2(\frac{n\pi}{a}x)dx Doing integration by parts i got to...

Hey! Is there an infinite ring with exactly two maximal ideals. Thanks in advance LiKeMath

Homework Statement The figure (found here) shows a cross-sectional view of two concentric, infinite length, conducting cylindrical shells. The inner shell has as an inner radius of a and an outer radius of b. The electric field just outside the inner shell has magnitude E0 and points radially...

I'm working on a calculus project and I can't seem to work through this next part... I need to substitute equation (2) into equation (1): (1): r\frac{\partial}{\partial r}(r\frac{\partial T}{\partial r})+\frac{\partial ^{2}T}{\partial\Theta^{2}}=0 (2): \frac{T-T_{0}}{T_{0}}=A_{0}+\sum from n=1...

Homework Statement A particle in an infinite box is in the first excited state (n=2). Obtain the expectation value 1/2<xp+px> 2. The attempt at a solution Honestly, I don't even know where to begin. I assumed V<0, V>L is V=∞ and 0<V<L is V=0 I tried setting up the expectation...

I am currently studying angular momentum and precession. If you suppose that you had a frictionless gyroscope with the flywheel spinning, thus precessing, could you harness the torque (converted to kinetic energy) generated about the axis of precession? since the force is generated by gravity it...

An "infinite potential box" This equation describes a particle in an "infinite potential box" with the width L, i.e.: Note that I do not know if it would be called an infinite potential box in English, but basically the particle can only be found within this space; outside of this the...

1. Homework Statement ∑ i=1 to n1+(1/i2)+(1/(1+i)2)−−−−−−−−−−−−−−−−−−−−√ = n(n+2)/n+1 2. The attempt at a solution First I did the base case of p(1) showing 3/2 on the LHS equals the 3/2 on the RHS. Then I assumed p(k) and wrote out the formula with k in it. Then prove p(k+1)= p(k)+...

Hi I don't understand the logic in the picture i added. They say that "that sum of the series = the limit of the sequence" The limit is 2/3 BUT the sum, Ʃ, must be 2*1/(3*1+5) + (2*2/(2*3+5) + 2*3/(2*3+5) ...+ Which is obviously much larger than 2/3 if all the terms are added together?? it's...

On the nature of the "infinite" fall toward the EH Observers Alice and Bob are hovering far above the event horizon of a block hole. Alice stops hovering and enters free fall at time T_0. Bob waits an arbitrary amount of time, T_b, before reversing his hover and chasing (under...

Homework Statement I am asked to prove that e^{iB} is unitary if B is a self-adjoint matrix. The Attempt at a Solution In order to prove this I am attempting to show e^{iB} \widetilde{e^{iB}} = 1. Using the assumption that B is self-adjoint I have been able to show that e^{iB}...