Infinity Definition and 970 Threads

Two charged particles are brought together from a great distance (r=infinity) to a distance of 2 m. The particle has a positive charge of 3.0 x 10^-5 C and the second has a negative charge of 1.35 x 10^-5 C. What minimum work was accomplished in this process? I can't for the life me figure...

Homework Statement Identify an=the summation from k=1 to n of (2n)/(4k2+1) as a Riemann sum of an appropriate function on an appropriate interval and find the limit as n approaches infinity of an. Homework Equations There is no interval givien so I assume its from 0 to 1. The...

Homework Statement We are asked to exhibit a measurable set E such that L^p(E) is separable for p= infinity. Also, we have to show that L^infinity(E) is not separable if E contains a nondegenerate interval.Homework Equations A normed linear space X is separable provided there is a countable...

Homework Statement Indicate whether sech(x) is invertible for [0, infinity) and explain why.The Attempt at a Solution Sooo... I know that: sech(x) = 2 / ( ex + e-x ) I know that to get the inverse equation I'd need to swap the y and the x... but I'm trying to show whether it's invertible...

Homework Statement Let \stackrel{lim}{_{n \rightarrow \infty}}a_{n} = \infty Let c \in R Prove that \stackrel{lim}{_{n \rightarrow \infty}} ca_{n}= \infty for c>0 (i) - \infty for c<0 (ii) 0 for c=0 (iii) Homework Equations Definition of divergence to infinity (infinite limit at...

let \infty = 1/0 then 1 =0 * \infty 0 = 0 * 1 then 0= 0 * (0*\infty) then 0 = (0* 0 )* \infty = 0* \infty =1 so 0 = 1 There is nothing called infinity

Hello, first time poster. I am putting this question in the PDE section because this was a question I came up while solving a PDE question. Also, I figured that since this is not a straight homework question, I can post in this category. Mods, feel free to move this post to wherever you...

Hello folks, I am on a project that involves combining Raman microscopy + optical tweezers, and I made a setup over the past year. All of this is home built on minimal funds so its not the neatest of all setups. It involves an upright microscope (coupled to trapping laser) and collecting the...

is it meaningful to evaluate cos and sin at infinity? I ask in relation to Fourier integrals... ie does cos(infinity) have a value

Please teach me this: What is the limit of [a]^{x} when [a]\rightarrow[/infinity] and[x]\rightarrow[/zero].It seem to me that it is divergent as lna,but I can not demontrate.It appears in the renormalization of Quantum Field Theory. Thank you very much in advanced.

f uniformly continuous --> finite slope towards infinity Homework Statement Given f:R \rightarrow R uniformly continuous. Show that \limsup_{x\rightarrow \infty} \displaystyle|f(x)|/x<\infty i.e. \exists C \in R: \, |f(x)|\leq C|x| as x \rightarrow \pm \infty. Homework Equations The...

Homework Statement Is it bad to put something like 0 < x < (inf) ? Since infinity is not a number. Homework Equations The Attempt at a Solution

I put this in the philosophy section but I guess it could equally go in a maths section being as I suppose it is the philosophy of maths. Infinities are well defined in maths, I doubt anyone could disprove given the set of all natural numbers then the set of all fractions is 1 to 1 and...

I'm trying to understand the set C_0(X), defined here as the set of continuous functions f:X\rightarrow\mathbb C such that for each \varepsilon>0, \{x\in X|\,|f(x)|\geq\varepsilon\} is compact. (If you're having trouble viewing page 65, try replacing the .se in the URL with your country domain)...

I am unsure as to how to prove a that as the limit as n goes to inifinity of a certain function the answer is 2.. I am trying to use the definition of a limit and using \epsilon and N - argument to get a contradiction in order to solve the equation.

I just read the chapter on entropy in my chemistry text. The book described entropy in terms of possible positions in space that a molecule could take (or even ways in which the atoms within a molecule can shift and rotate). The claim was that gasses had higher entropy than liquids and liquids...

Complex numbers - "parallel lines meet at infinity"? What does it mean? We started learning about complex numbers last week. One of the first things my teacher said was that "We learned that parallel lines never meet. But as it turns out, they meet at infinity." I'm willing to accept it...

Homework Statement How much work is needed to arrange three charges, Q, into an equilateral triangle? The particles are initially infinitely far apart. Take 'a' to be the length of each side of the triangle. Homework Equations U = {(kqq)/L} The Attempt at a Solution I was under...

Homework Statement The figure below shows three charges at the corners of a rectangle of length x = 0.55 m and height y = 0.35 m. http://www.webassign.net/walker/20-23alt.gif (a) How much work must be done to move the +2.7-µC charge to infinity? Homework Equations W=(\DeltaV)(q)...

Homework Statement The figure below shows three charges at the corners of a rectangle of length x = 0.55 m and height y = 0.35 m. http://www.webassign.net/walker/20-23alt.gif (a) How much work must be done to move the +2.7-µC charge to infinity? Homework Equations W=(\DeltaV)(q)...

Hi guys, I have a little problem with this question: Determine the limit (x approaching infinity) \frac{|9-3x^{2}|}{x-2x^{2}} (Sorry, I'm not sure on how to use the Latex feature) Anyways, I've combed the forum and found a couple of threads that are somewhat related to my problem...

Homework Statement Two point charges -2Q and +3Q are on the x-axis at the origin and at x = L. Find all the points on the x-axis (not at infinity) where the electric potential is zero. Express your answers in terms of L and Q.Homework Equations V= k*Q/rThe Attempt at a Solution I understand...

Gday, I was contemplating limits today and tried to prove something to myself and I can't figure it out. This is what I am trying to wrap my head around. http://latex.codecogs.com/gif.latex?\lim_{x \to \infty } \sqrt{x^2 + 1} I'm not looking for the "numerical" solution of infinity...

I've gotten claims that infinity is not a number but an idea. How do infinities work in operations? Are there "smaller" and "bigger" infinities? If ∞+1=∞, is ∞-∞=1?

We often have lim_{x\rightarrow a}f(g(x)) = f(lim_{x\rightarrow a} g(x)) if f(x) is continuous at g(a). But then my question arises where g(x)\rightarrow\infty. I am not sure if there is any meaning to continuity at infinity as it seems that continuity is the property of a particular...

Homework Statement The figure below shows three charges at the corners of a rectangle of length x = 0.35 m and height y = 0.22 m. http://www.webassign.net/walker/20-23alt.gif (rectangle image) (a) How much work must be done to move the +2.7 µC charge to infinity? (b) Suppose...

Homework Statement Find the following limit: \lim_{x \to \infty} \frac{2+\sqrt{(6x)}}{-2+\sqrt{(3x)}} Homework Equations n/aThe Attempt at a Solution I know this shouldn't be that hard, but somehow I keep getting stuck on simplifying the equation. I think the first step is to multiply both...

'show that the entropy change of the object tends towards deltaQ/T (subcript i) as its mass tends to infinity, in the4 limit where it becomes a heat bath i got: change in entropy =mc ln (Tf/Ti) (mc ln (T subcript f/T subcript i)) but if the mass tends to inifinity...

I was wondering the following two situations: 1) If x is a real variable, then, is it correct, or is it acceptable rigorously to assign x x = +infinity ? 2) if x is not necessary a real variable, then is it correct, or is it acceptable rigorously to assign x x = +infinity ? I am...

Homework Statement <In Pic 1> Homework Equations (1/2)mv2 = ΔU The Attempt at a Solution I thought that if i apply the equations i'll have my answer but i got 2.5m/s while answer is 3m/s Please refer the solution given by some book --- Pic2, Pic3 <sorry for bad image, my...

Homework Statement Evaluate the following limits: lim sqrt(x^2-3x+1)-x x->\infty lim sqrt(x^2-3x+1)-x x->-\infty 2. The attempt at a solution http://img816.imageshack.us/img816/9995/limitproblem11.jpg We have to enter in the answers online into a program that tells us if...

I'm reading a lot of stuff about the expanding universe, and also about it being infinte. So now I was wondering: How can the universe expand while it's infinte? (or am I asking something that nobody really know's the answer to?)

Homework Statement hello, the problem is that i have charge q which lies in d distance from a plane and I need to find function \sigma which describes density of this charge The Attempt at a Solution I wrote this situation in cylindrical coordinate system where q lies in point A=(0,0,h) and...

Can you have infinity plus or minus one? Assuming infinity is possible of course.

Hey, is infinity a concept or an actual number? This is a discussion with someone, I say it's a concept but then he brought up set theory, and I have no set theory knowledge whatsoever.

Compute \int^{\infty}_0 \frac{x^{\alpha}}{1+x^2} dx for some -1<\alpha<1. EDIT: This was slightly wrong. The hint given is that we can integrate from -p to p except for a small semi-circle around 0, and a large semicircle from p to -p, and choose a branch of z^{\alpha}. Wouldn't this in...

Hi, I am wondering what happens to a Gaussian distribution when its mean tends to infinity. By looking at the equation of a Gaussian one might infer that the limit will go to zero; but does this imply that it reduces to a Dirac-Delta function? More precisely, if we integrate this limit we...

y=1/2(sinx-cosx+e(^pi-x)) question: if x approaches infinity, which term or terms will dominate? from my understanding, sinx and cosx will oscillate and the e term will approach zero. so would the answer be sinx-cosx? please and ty

Is it so that for limx->infinity f(x) to exist , limx->+infinity f(x) and limx->-infinity should exist and be equal ? if so then why ?

Hi, i need to solve this integral : \int _{0}^{\infty }\!{\frac {x}{{{\rm e}^{x}}-1}}{dx} i solved it using series and i got the right answer of Pi^2 / 6 but i need a solution using complex analysis i need help with finding the right contour for this problem. i tried change of...

Homework Statement Define a sequence (fn) from n=1 to infinity of functions on [0,1] by fn(t)=t^n does the sequence converge in (CL^2[0,1],||.||2) Homework Equations The Attempt at a Solution I am struggling on where to start. I am fairly new to the L2 space and so would just...

Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...

Evaluate the following integral from 0 to infinity. (see attached for better picture) e^(-ax)-e^(bx) ------------------ dx x Remarks: a , b > 0 a < b

I'm revising my course text for my exam and came across a Fourier series problem finding the Fourier series of the square wave: http://img574.imageshack.us/img574/5862/eq1.png. It is then calculated that the complex Fourier coefficients are...

Is "Infinity" only a mathematical concept or is there anything infinite in reality? I mean ∞ is indeterminate in a way such that any of the following expressions can be constructed: ∞ - ∞ = 1, ∞ - ∞ = 0 ∞ - ∞ = ∞ Is there anything in reality that can actually behave like that?

Homework Statement \lim_{x \to \infty} \sqrt{x}\sin\frac{1}{x} Homework Equations I don't think you can use the squeeze theorem here...The Attempt at a Solution So I am just studying for an exam that I have tomorrow and I am going through problems that weren't assigned on our homework set...

I am working on a proof in which I have an integral with bounds negative infinity to zero, with an even function, i.e., f(y) = f(-y). I took the limit to infinity rather than negative infinity since y is negative (which is OK I think) but now I have an integral that goes from infinity to 0. What...

Does e^[(-infinity)+(i*w*infinity)] = 0 or 1? w = omega

Just as the title states, I'm working on a problem and have come to negative infinity divided by infinity. Is this an indeterminate form? I know that if they are both positive it is indeterminate, but I can't remember if one being negative makes a difference.

Hello everyone...I was wondering if it is possible to conceive a 2nd center of a finite sphere in infinity...(I am not a mathematician and therefore, my words might look ridiculous) apparently, it looks like every point on the sphere is at the same distance from infinity...Anyway, this...