What is Infinite: Definition and 1000 Discussions

So I'm trying to get through euler's introduction to the analysis of the infinite so I could eventually read his books on calculus but I'm stuck somewhere and can't seem to figure out how he equates this identity so by expanding I get sin(2y) * cos(z) + cos(2y) * sin(z). I get that the...

Is this true? Because if it were infinite, how would it start at a small singularity? I mean it didn't start out at a finite size then grow to infinity right?

An electron in the ground state of a one-dimensional infinite square well of width 1.10 nm is illuminated with light of wavelength 600 nm. Into which quantum state is the electron excited? ok so I first calculated the engery of the electron in the first ground state of the square well...

Hello, this is not a homework assignment. I am referencing an old assignment from a few semesters ago. I am curious if I can use the basic:dB = mu/4pi dq * v X r /r^2; where dq = sigma*da=sigma*L*dx; instead of just using Amp's Law. this stuff was fun...dunno if i was at all correct...

Homework Statement Solve for the wavefunctions and energy levels of an infinite square well potential extending between -L<x<L. Hint: It may be worth noting that for a potential symmetric in x, then the observed probability density must also be symmetric in x, i. |ψ(x)|2 = |ψ(-x)|2. Homework...

Homework Statement I need to fin the sum of the following two infinite series: 1. Ʃ[n=0 to ∞] ((2^n + 3^n)/6^n) and 2. Ʃ[n=2 to ∞] (2^n + (3^n / n^2)) (1/3^n) Homework Equations use the sum Ʃ[n=2 to ∞] (1/n^2) = ∏^2 / 6 as necessary The Attempt at a Solution I tried to manipulate them...

Homework Statement I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges: ∑ sin(1/n^2) from 1 to ∞ Homework Equations Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists: L =...

Before I say the exact question, this is a inquiry about a hypothetical situation that says the Universe is infinite in both size and age. If possible, I would like a full explanation to what happens to the Universe going beyond the specific question, but I have the question here basically as a...

Hello, i have been watching documentaries and reading papers about the universe and I've noticed that there are many opinios on the size of the universe. Some say it's infinite and some say it's not. But if it's not, then it has to have a center. So my question is, is the universe infinite or...

Suppose we have a thick slab with a current density J pointing strictly in x direction...see below link for figure: http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter5/LectureNotesChapter5056.jpg what is direction of magnetic field inside? It is easy for me to see that...

Test these for convergence. 5. infinity E...((n!)^2((2n)!)^2)/((n^2 + 2n)!(n + 1)!) n = 0 6. infinity E...(1 - e ^ -((n^2 + 3n))/n)/(n^2) n = 3 note: for #3: -((n^2 + 3n))/n) is all to the power of e Btw, E means sum. Which tests should I use to solve these?

Test these for convergence. 3. infinity E...((-1)^n)*(n^3 + 3n)/((n^2) + 7n) n = 2 4. infinity E...ln(n^3)/n^2 n = 2 note: for #3: -((n^2 + 3n))/n) is all to the power of e Btw, E means sum. Which tests should I use to solve these?

Test these for convergence. 1. infinity E...n!/(n! + 3^n) n = 0 2. infinity E...(n - (1/n))^-n n = 1 Btw, E means sum. Which tests should I use to solve these?

If you draw a graph representing the tapering of gravitational force with respect to distance between two point masses (by the inverse square law y=x<exp-2>), the gravitational energy between two points would be the area under the graph between those points. This is my assumption. Now the...

I was trying to calculate the the charge distribution (surface charge density = σ in function of r) in a very long circular metallic plate. I know σ not constant if we get closer to the rim of the plate Let's say we want to calculate the E field in point Q that is x distant from the center...

Here is the question: Here is a link to the question: Abstract math question: bijectivity on finite and infinite sets? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Evaluate the indefinite integral as an infinite series ∫ sin(x2) dx Homework Equations The Macluarin series of sin x = ∞ Ʃ (-1)nx2n+1/(2n+1)! n=0 The Macluarin series for sin(x2) = ∞ Ʃ (-1)x4n+2/(2n+1)! n=0 The Attempt...

Hi, I've been reading a textbook on set theory and came across Cantor's proof of the statement that the set of the infinite binary sequences is uncountable. However there is one thing that is not clear to me: The nth such sequence would be: An = (an,0,an,1,...), n = 0, 1, 2,... where...

Hi there, 2nd year student, absolutely stumped on this don't even know where to begin. [I]"Determine the vector potential due to an infinite cylinder of radius, R, carrying a uniform current density, j. Use this to describe the magnetic field inside a current carrying wire I am using...

Homework Statement Hey guys:) Maybe you will be able to help me with this problem i got as an assignment for my quantum mechanics course, it goes as follows: a particle of mass m moves in the potential for x<0 infinity, for 0<x<a -U, for a<x<b 0, for b<x infinity. a) Sketch the...

For the series such that: \Sigma _{n=1} ^{\infty} a_n =\Sigma _{n=1} ^{\infty} b_n A certain theorem says that these series are equal even if a_n = b_n only for n>m. That is, even if two infinite series differ for a finite number of terms, it will still converge for the same sum. I am thinking...

Hey guys, what sup I need you all to help me in resolving the integral of an infinite product... i was thinking of perhaps integrating by parts, but when yo do that the integration becomes brutally expansive... any ideas? thank you all very much the variable which is aimed to be integrated is x...

Homework Statement ∞ Ʃ (-1)^(k+1) / kln(k) k=2 Homework Equations integral test, p test, comparison test, limit comparison, ratio test, root test. The Attempt at a Solution In class so far we have not learned the alternating series test so i can't use that test. So far I have...

Homework Statement A filamentary conductor carrying current I in the az direction extends along the entire negative z axis. At z=0 it connects to a copper sheet that fills the x>0,y>0 quadrant of the xy plane. (a) Set up the Biot-Savart law and find H everywhere on the z axis; (b) repeat part...

If $\displaystyle y=\frac{3}{4}+\frac{3*5}{4*8}+\frac{3*5*7}{4*8*12}+...\infty$. Then $y^2+2y = $

∞ ∫ x^3 dx =∫ x^3 dx+∫x^3dx -∞ I split up integral and got (x^4)/4 and infinity when evaluating using limits. does the integral converge to zero or diverge to infinity minus infinity? would really appreciate help answering this question. Thanks

∞ ∫ x/(x^2+1) dx -∞ I basicaly evaluated the integral and Ln (x^2+1) as the antiderivative and when taking the limits I get ∞-∞ (ln |1| -ln|b+1|) + (ln|n+1|- ln|1|) lim b-> neg. infinity lim n-> infinity does this function converge or diverge? this was a question on...

Homework Statement Use Gauss's Law to calculate the field of an infinite plane sheet of surface charge density σ0. Homework Equations The Attempt at a Solution The solution is, where A=area: 2EA=(σ/ ϵ0)A E=σ/2ϵ0 Why is there a '2' in the solution? I know it's...

How to make a surface plot involving an infinite series in Matlab Solving Laplace's equation for electric potential for a 2D surface yields: V(x,y) = 4 Vo/pi * Ʃ (n=1,3,5,...) (1/n e^(-npi*x/a) sin(n*pi*y/a) ,where a is and Vo are constants ...it's convoluted, but basically, I need to...

Homework Statement Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 4.2 cm. Each sheet consists of an infinite array of wires with a density n = 16 wires/cm. Each wire in the left sheet carries a current I1 = 2.3 A in...

I have a vague understanding of how to derive the sine function from a Maclaurin Sequence however this isn't helping me figure out why: (1 - \frac{x^{2}}{4π^{2}}) (1 - \frac{x^{2}}{9π^{2}}) (1 - \frac{x^{2}}{16π^{2}})... = \frac{π^{2}}{x(x+π)}\frac{sin x - sin π}{x - π} Any help would be...

Homework Statement Two problems: 1) We're given a probability distribution function with possible values and their probabilities of occurring: X=1, P = .67 X=2, P = .19 X=3, P = .05 X=4, P = .04 X=5, P = .03 X=6, P = .02 And we need to find P(XBAR >=6) and P(XBAR >=5). I don't...

Dear Sir, If we consider the Big Bang Hypotesis , the age of the universe and the rate of expansion ogf space, the Universe could be very large , but finite. But Prof Sean Carrol said , in a lecture , that there's a possibility of Infinite Universe. Please elaborate.

Morning everyone, I apologize for bringing up a topic that has probably been discussed to death here in the past. I've been reading the FAQ, and a few old threads about finite vs infinite universe, but I'm still struggling to grasp both of these ideas. I'd be really grateful if someone could...

Homework Statement Recalling that the field due to an infinite line charge with Charge-per-unit-lenght λ is E=λ/2∏εx At distant x from the line, find the field due to an infinite "Ribbon" of charge 2cm wide, at point 2 cm from one edge in the plane of the Ribbon. The surface charge...

I have been reading up on time dilation a bit this morning, and for the first time, I think it really clicked. Its raised some questions that I haven't seen answered anywhere, so I was hoping someone here could help. As I understand it, and please correct me if I am wrong, the only thing that...

I heard this question from my TA and was not satisfied with the answer. Can someone elaborate for me please? There are two infinite lines of current that are traveling in the same direction. By the right hand rule and ampere's law, we can calculate the magnetic field and calculate the F of...

I am just trying to figure out how to make a CW complex for this. For the n-genus orientable manifold (connect sum of n-tori) I feel like a lot of things make sense, fundamental group, CW complex, etc. But in the infinite case, things seem to fall apart. For example, I can not figure out how...

I recently watched a video by SpaceRip on YouTube addressing whether or not the Universe is infinite. They mentioned an example as to why it isn't briefly, but didn't expand on it. I kept thinking that its a good reason and I want your opinion on it. Since Newton's law of universal gravition...

Hi there. I have just been doing some reading on manifolds, and I'm finding some of it hard to grasp. An example we were given was of the infinite cylinder and how to construct its map, and that it would be with one chart. the reading initially says that we can use θ \in (0,2pi] and z \in...

Homework Statement What are the electric and magnetic fields due to an infinite sheet of surface current \vec{K} = \hat{j}Ko in the plane x=0? The plane is electrically neutral and Ko is a constant. Plane electromagnetic waves are APPROACHING the plane x =0 from either side, incident normally...

Homework Statement Consider an infinite charged line along the z-axis, with linear charge density . The charge moves uniformly with velocity v in the positive z direction. 1. Give an expression for the electric and magnetic field. 2. Give an expression for the energy flux density (or energy...

Assume for some real number L and c \displaystyle\lim_{x\rightarrow c} f(x) = ∞ and \displaystyle\lim_{x\rightarrow c} g(x) = L We must prove \displaystyle\lim_{x\rightarrow c} [f(x) + g(x)] = ∞ Let M > 0. We know \displaystyle\lim_{x\rightarrow c} f(x) = ∞. Thus, there exists...

Homework Statement ∫e-Sxsin(ax) dx, S and A are constants, upper limit is ∞ lower is 0 Homework Equations ∫ u dv = uv - ∫ vdu The Attempt at a Solution After integrating by parts twice I got: (S2)/S(S2+a2) lim c→∞ [-sin(ax)e-Sx + acos(ax)e-Sx] |^{C}_{0} Okay, now how on Earth do I take...

Homework Statement True or False? Every infinite group has an element of infinite order. Homework Equations A group is a set G along with an operation * such that if a,b,c \in G then (a*b)*c=a*(b*c) there exists an e in G such that a*e=a for every a in G there exists an a' such...

For potential well problem for well with potential which is zero in the interval ##[0,a]## and infinite outside we get ##\psi_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}##. If I want to get this result for well with potential which is zero in the interval ##[-\frac{a}{2},\frac{a}{2}]## and...

Homework Statement A long hairpin is formed by bending an infinitely long wire, as shown. If a current of 1.20 A is set up in the wire, what is the magnitude of the magnetic field at the point a? Assume R = 3.20 cm...

Homework Statement Find the values of k in the following system of linear equations such that, the system has no solution, the system has a unique solution, and the system has infinitely many solutions. x+y+2kz = 0 −2x−y+6z = −3k −x+2y+(k2 −3k)z = 9 Homework Equations The...

I have to prove that the cardinality of the set of infinite sequences of real numbers is equal to the cardinality of the set of real numbers. So: A := |\mathbb{R}^\mathbb{N}|=|\mathbb{R}| =: B My plan was to define 2 injective maps, 1 from A to B, and 1 from B to A. B <= A is trivial, just...

Homework Statement Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third energy level, E3, to the lowest energy level, E1. Homework Equations E_n = \frac{\left (n_{x}^{2}+n_{y}^{2}+n_{z}^{2} \right) \pi^{2}...