Infinity Definition and 970 Threads

Hi everyone, once I again I turn to all of your expertise in complex analysis. Homework Statement Evaluate \int\frac{(ln(x))^{2}}{1+x^{2}}dx from 0 to +infinity by appropriate series expansion of the integrand to obtain 4\sum(-1)^{n}(2n+1)^{-3} where the sum goes from n=0 to...

Homework Statement Find the limit as x approaches infinity of (the square root of x^2 + x minus the square root of x^2 -x) Homework Equations The Attempt at a Solution I do not know how to simplify the expression. I know that plugging in x = inifinity would be wrong. How...

Homework Statement hey there I have been given a question that asks me to define a sequence Xn which tends to infinity that has a limit that is infinity! I am so cofused. I would assume to use an adapted version of the epsilon delta condition? Homework Equations It's for Analysis...

I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why? This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't...

One of our senior teachers talked about infinity and said that 1∞ is not defined. On deeper probing, he said that it is a bit higher mathematics and it wouldn't be appropriate to go deeper here. Naturally, I could think of a inductive proof that it should be 1, if ∞ ∊ N. I can't think of a...

\int_0^\infty \lambda x e^{-\lambda x} dx How do I use the limits (infinity and 0) after getting the equation from integration by parts?

I hope that this is thr right place to post this. If I walk down an infinite yellow brick road, flipping a fair coin with each step, and taking a step to the left if tails, a step to the right if heads, it would seem possible that I could end up a trillion miles from the road's centerline...

Find the limit of \frac{2^n}{n!} when n approaches infinity.

Assuming a system with relatively small but non-negligable mass falling from infinity to a maximally massive black hole; Would there be a maximum possible coordinate velocity below c ? Is it possible to do an approximate calculation for this? A ballpark figure?? If there is a...

Homework Statement Show lim n^{1/2}=\infty using the definition of lim x_{n}=\infty. Homework Equations The Attempt at a Solution We want to show \left|x^{1/2}-\infty\right|,\epsilon. I get this far and i hit a blank.

I am starting this thread because when I was doing a homework problem I got interested in something: \lim_{x \to +\infty} x^\frac{1}{x} I already know that the answer is one because \frac{1}{\infty} is the same as 0 and anything to the zeroth power is 1. The thing that got me interested is...

Homework Statement lim (x→pi)〖sin(x-pi)/(x-pi)〗 Homework Equations i don't know if we should use trig identity sin(a-b)= sinA cos B- CosA sin B The Attempt at a Solution i use identities to solve that, i did not get the answer. i tried to multiply by conjugate, did not work also.

Cantor's s(w)et :) Hi! I don't know if this makes any sense, but after reading the book "Pi in the Sky" this summer (It got really exceptionally hot here in high latitudes) I was let wondering the following: Let C be the number of the continuum of numbers (with decimals). Let N be the...

I think about on this and found a result, e^{i\pi k}=e^{-i\pi k}=-1\Rightarrow i\pi k=ln(-1) a>1 and k=1,2,3... y=(-a)^{i\alpha }\Rightarrow lny=i\alpha ln(-a)=i\alpha (ln(-1)+lna)=i\alpha (i\pi k+lna)\Rightarrow y=e^{-\alpha \pi k}e^{i\alpha \ln{a}} Then \alpha \ln{a}=-\pi...

This post is in cosmology (not number theory, eg, Cantor) because our only (main) exposure to infinity is astronomical. Folks have used infinity to predict that another ClamShell has or is or will be typing this message...ballderdash...it would take an infinity of infinities for this to...

Excuse the typing please, as I am posting from my phone. Let f have domain [0,infty) and range in R. Suppose as x goes to infinity, f'(x) goes to a constant b. I wish to show that f(x)/x goes to b as x goes to infinity. I have tried numerous applications of the MVT to solve this and cannot...

Homework Statement Hi, I need to figure out what happens to this equation in the limits E = \frac{1}{4\pi\epsilon_0} \frac{2\lambda L}{z \sqrt{z^2+L^2}} in the two different cases that z>>L and when L -> infinity (note this equation was derived from finding the electric...

when the smallest particle is cut in half over and over again infinitely times, it will never disappear... since I used the word infinite, right?

Is there a way to make sense of the following statement: "f is continuous at a point x_0 such that f(x_0) = \infty?" The standard definition of continuity seems to break down here: For any \epsilon > 0, there is no way to make |f(x_0) - f(x)| < \epsilon, since this is equivalent to making...

Homework Statement Eight 3.0 μC charges are located at the corners of a unit cube centered about the origin with 1mm edges. How much work does it take to bring a 5.0 μC charge from infinity to the origin? Homework Equations U= k*q1*q2/r The Attempt at a Solution r=...

I've had my second class of Modern Physics and I have some "obvious" doubts that many of you certainly had, although I didn't find anything answering the first doubt on a quick google search. 1)Say I am in an inertial reference frame. I can see that any photon going around me do it at a...

Homework Statement The lenses are separated by 250mm. Where should the object be places so that the final image is formed at infinity? I'm confused.

or 1 = infinity Discuss

I read in a book that if an electron is beyond infinity from another charge particle, then its potential energy will be positive :/ Please tell me which formulae are used for potential energy beyond infinity??

Are there general boundary conditions for the wave equation PDE at infinity? If there is, could someone suggest a book/monograph that deals with these boundary conditions? More specifically, if we have the following wave equation: \[ \nabla ^2 p = A\frac{{\partial ^2 p}}{{\partial t^2...

The program Wolfram Alpha say "True" but my friends want the Proof. Could you help me please?

In both http://en.wikipedia.org/wiki/Dynamical_billiards" we have a potential who's value is infinity. Now if it were just a finite number (rather than infinity), I would be getting a dirac delta function in the equations of motion (I think..) but when it's infinity I can't really do...

I know that 1^(+/- infinity) is indeterminate. Is c^(+/- infinity) indeterminate for real numbers c?

I've been thinking about getting a tattoo. I was considering getting the infinity symbol inside of an absolute value. Or the absolute value of infinity. Whichever you prefer. How mathematically correct is that? The absolute value of infinity simplified is infinity is it not? Will I completely...

Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in...

[FONT="Fixedsys"]Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number...

Does this reasoning ever reach infinity? 0<1<2<3<4<5... What does it mean? Thanks!

I was just thinking about how division by zero is undefined and began wondering if dividing by infinity is undefined as well. I understand the limits that accompany this idea...

Hi, I came across a book which looks at a problem like \lim_{x \to 0}\frac{1}{x} So you approach from 0-, and get -∞, approach from 0+, get ∞ Then it would write the answer as \lim_{x \to 0}\frac{1}{x} = \left| \infty \right| It looks bizarre to me. How do you parse this? Is...

Ok so I was watching this program on TV and the guy ended up getting r=0 With this he put this value into the equation as so: 1/r = 1/0 = infinity What is up with that? Isn't it undefined. Also, this is about black holes.

Hi, I have a second order DE involving the first derivative and with singularities at zero and at infinity. I need the approximate behavior at zero and at infinity. I have the answer but I would like to know how to get there. I don't know how to start this search. Any help?

This is not a homework assignment but a question from a past exam paper as i am studying for an exam on monday. I am one of only 3 out of 150 who have never done physics before this, the first year of an electronics degree. I would really appreciate any help. 1) A charge q1=1e-4C is in a...

Homework Statement Compute lim as x goes to infinity of (1+1/x^2)^x Homework Equations I know that lim at infinity (1+1/x)^x=e I do not know if that is still valid with the x^2 there. I don't really think it is, but it's throwing me off. The Attempt at a Solution Beyond the...

Homework Statement Find the limit: an= 2n/(n2+1)1/2 Homework Equations n/aThe Attempt at a Solution Because n is approaching infinity, is it OK to disregard the +1 in the denominator and just consider the denominator to be n? This would then divide out the n in the numerator leaving 2...

Homework Statement Hi, I need to find the Fourier Transform of: g(t)=\frac{1}{x}e^{\frac{-\pi t^2}{x^2}} Homework Equations G(f)=\int_{-\infty}^{\infty }g(t)e^{-j2\pi ft}dt \therefore G(f)=\int_{-\infty}^{\infty }\frac{1}{x}e^{\frac{-\pi t^2}{x^2}-j2\pi ft}dt The Attempt at a Solution...

Hey guys I am working on a Physics problem and can't figure out a little but of math involved. What is this integral? I tried it out and got "1/a + a", assuming "1/a" is the positive half of the integral.

I can not understand what to do with this Lim 1/2^x-1 as x goes to infinity. i tried using l'hopitals rule but it does't work or I am not applying it right.

A difficulty I'm having is that PE, at least in the context of gravity, is said to go up with altitude, or distance from the gravitational source (the analogy of pushing an object upward against the force of gravity and thus adding PE to it). Yet PE drops to zero at infinity, which would seem to...

Is infinity merely a mental concept, or is it entirely meaningful and common? :confused: Infinity does not exist in the context of a number system. Example: what would infinity minus 1 be? It's not infinite since no finite number plus one equals infinity. We see that the rules of arithmetic...

Homework Statement I am required to express in \varepsilon - \delta way what I'm suppose to prove in case lim_\below{(x \rightarrow \infty)} f(x) = \infty Homework Equations None. The Attempt at a Solution So first, intuitively I thought that what this means is that f(x) is bigger...

how this thing works ? integration of e to the power of (-x) from 0 to infinity sorry , not good in using the symbols ..^.^ ~

Homework Statement Consider the power series. sigma (n=1 to infinity) x^n / [n(n+1)] if f(x) = sigma x^n / [n(n+1)], then compute a closed-form expression for f(x). It says: "Hint: let g(x) = x * f(x) and compute g''(x). Integrate this twice to get back to g(x) and hence derive...

Homework Statement Using the fact that the integral from -Infinity to Infinity of e^-x^2 is equal to Sqrt(Pi), find the integral from -Infinity to Infinity of x^2 * e^-x^2 Homework Equations The Attempt at a Solution I really don't know how to find this using the fact that...

Infinity has always been a problem for me, apart from the concept I do not believe it exists. numbers go on to infinity and even negative infinity but they don't really exist so they don't count (hehe). some people say the universe is infinite in size. well apart from infinite in the same way as...

1. Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity I'm trying to understand how to use Fourier Transforms to solve Definite Integrals with limits from 0 to Infinity. I understand how to use Fourier Transforms to solve indefinite integrals, but I believe there...