Infinity Definition and 988 Threads

Why is gravitational potential energy defined at infinity? Like here on Earth there is Zero potential energy at the center of the Earth (if you could theoroeetically go there) so why not define it as 0 at zero distance from the force supplier instead of at infinity? I understand why the...

hey pf! can someone shed some light on why odd integrals don't necessarily converge over infinite symmetric domains? thanks!

Homework Statement 180\int_5^\propto \frac{2}{(4+x^{2})^{3/2}} dx Homework Equations Trigonometric Substitutions: (x=2 tan z). The Attempt at a Solution I've computed the integral and ended up with 180 [\frac{x}{2(4+x^2)^{1/2}}] from 5 to infinity. I could've easily computed...

Two of the posible spatial hypersurfaces in FRW cosmology(the flat one and the negative curvature one) are infinite in extensión. I'm not entirely sure how is a finite energy density for the universe obtained as energy/volume if the volume is infinite. I know it is easily computed with the...

Hi, I was wondering why the one and infinity norm of a complex vector x are not equal to the the one and infinity norm of x* (the conjugate transpose of x)? This seems to be true for the 2-norm, but I am not sure why for these other norms.

https://dl.dropboxusercontent.com/u/260388836/index.html Let arrow height be 1cm. focal length:1cm So if I move the arrow to the focal point,image is not formed.(i.e formed at infinity) But, Lets move it to say 0.999 Now the image is virtual and is magnified to about 1000X If I make it...

Homework Statement Prove the following result: \frac{1}{2.2} + \frac{ 1}{3.2^2} + \frac{1}{4.2^3} ... = 2ln2 -1 Homework Equations The Attempt at a SolutionI tried writing down the nth term of the series which is 1/(n+1)2^n But don't know where to move after this.

Homework Statement Sum to infinity \frac{1}{2!} - \frac{ \pi ^2}{4^2.4!} + \frac{\pi^4}{4^4.6!} ... Homework Equations The Attempt at a Solution I thought the series was similar to the Maclaurin expansion of cos x so I tried putting in x= ∏/4 But I end up with the...

How do you tell if a limit is infinity, and you should use that approach, or if you should try to factor/multiply by congegate, etc.? Do you use the latter if its 0/0 and the first if its a number/0 when you try pluging in th limit?

\displaystyle\sum_{n=1}^{\infty}{n} = {-}\dfrac{1}{12} It seems that, regardless of intelligence, this proof (or sum, or proof of sum, or demonstration of sum) rattles some more than others. It is so astoundingly counter-intuitive that embracing it means really leaving your mathematical...

Homework Statement ΔABC has AB= 8 in, BC= 10in , CA= 6in . AD is the perpendicular from A to BC. DE the perpendicular from D to AB, EF the perpendicular from E to BD and so on. Show that CA + AD + DE+... is a geometric series and find it's sum to infinity. Homework Equations The...

Homework Statement integral (e^-ax)sin(bx) from 0 to infinity Homework Equations The Attempt at a Solution I want to check if my answer is right I got \frac { \frac { -1 }{ a } { e }^{ -ax }\quad sinbx\quad -\frac { b }{ { a }^{ 2 } } { e }^{ -ax }\quad cosbx }{ 1+\frac {...

Simple question; Why isn't it \sum am (from m=1 to infinity) Thanks in advance.

(1) Evaluate the limit as x goes to infinity using L'Hospital's rule: 8xe^(1/x)-8x (2) L'Hopital's Rule (3) How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new...

This is something that has bothered me for some time, and I can't seem to find any threads on here about it. In a lot of my undergraduate courses in physics, we talk about integrating something physical to infinity. For example, in electrostatics, we talk about the work needed to assemble a...

Homework Statement Determine limA→∞(sinc(x/2A)) Homework Equations I would use L'Hôpital's rule, but I'm not sure if it is valid in this case as the function is that of x, not A. I want to know if it's valid to treat x as constant and take derivatives with respect to A and evaluate as...

Homework Statement delta dirac function(x) * e^(-i*x) at ∞ and -∞ Homework Equations delta dirac(x)*e^(i*x)The Attempt at a Solution I'm wondering how e^(i*x) looks like at infinity/-infinity. I know it has some sort of oscillating property i.e e^(pi*i)=e^(3pi*i). The problem is I'm trying to...

If something is strictly less than something else, is it definitely finite? Because if x < y, and the biggest thing y can be is ∞, then x < ∞, but does that mean x is finite? Couldn't x = (∞ - 1)? Isn't that still technically infinity? What if x = (∞ - ε)?

Homework Statement prove that ##\lim_{x \to \infty} \frac{\sqrt{x+1}}{x} = 0## where ##x>0## Homework Equations Definition: Let ##A\subseteq\mathbb{R}## and let ##f:A\rightarrow \mathbb{R}##. Suppose that ##(a,\infty)\subseteq A## for some ##a\in\mathbb{R}##. We say that...

Homework Statement http://i.minus.com/jbwNvxhmIxeKxB.png The Attempt at a Solution I'm unclear on whether the entire log is being squared or if just the (1-x) term in the denominator is being squared. I know if it's the latter, then the exponent can be moved to in front of the log.

I know I am already boring with limits,but i again have two of them to deal with and i don't know how... 1. \lim _{n \to \infty} \frac{5^{n^+1}-2*5^n+5^{n-1}}{3^{n+1}-3^n} 2. \lim _{n \to \infty} \frac{\sqrt[3]{n^4}+\sqrt{n}+1}{\sqrt[6]{n^4}+\sqrt[3]{n}+2}

Again i have two similar problems: \lim _{n \to \infty} \frac{3n-\sqrt{4n^2+n}}{3n+\sqrt{4n^2-n}} \lim _{n \to \infty} \frac{\sqrt{9n^2-n}-2n}{\sqrt{9n^2-n}+2n} Those kind of problems will be on my exam,which is very close,and i don't get it how to deal with this limits... I just say...

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox? If it does have a physical existence why don't we come across any quantity which is physically eternal? Someone please help..

If there is an actual infinity of throws of two dice, would all combinations have the same probability (that is each combination would happen an infinite amount of times)?

If you have f(x) = 1/x and g(a) = (cosx - 1)/x and then y = [limx→0 f(x)][limx→0g(x)], the two individual limits equal 0 and infinity, respectively. Since these are limits and only approach these values, would the multiplication of the two limits equal 0, infinity or something else?

Laurent series at infinity point I already calculated it, but my work was too long, I really wish to find a shorter route. Calculate the Laurent series of \frac{1}{(z^{2}+1)^{2}} around z_{0} = 0 First, I used simple fractions and I got: \frac{1}{(z^{2}+1)^{2}}=\frac{-i}{4} \frac{1}{z-i} +...

Homework Statement Prove Ʃ1/(n^2) as n goes to infinity = (∏^2)/8 Homework Equations The Attempt at a Solution No idea how to start. Pls guide. Thanks

My question is: Show the limit of x_{n}=\frac{ln(1+\sqrt{n}+\sqrt[3]{n})}{ln(1+\sqrt[3]{n}+\sqrt[4]{n})} as n approaches infinity Solution: {x_n} = \frac{{\ln (1 + {n^{\frac{1}{2}}} + {n^{\frac{1}{3}}})}}{{\ln (1 + {n^{\frac{1}{3}}} + {n^{\frac{1}{4}}})}} = \frac{{\ln \left(...

1. Evaluate lim x\rightarrow-\infty \sqrt{x^2+x+1}+x.The answer is -\frac{1}{2}. Homework Equations None. The Attempt at a Solution I multiplied by the conjugate first, so it turns into lim x\rightarrow-\infty \frac{(x^2+x+1)-x^2}{\sqrt{x^2+x+1}-x} = lim x\rightarrow-\infty...

Hello, I'm fiddling with Wolfram Alpha and I can't find a definition of what do they mean by the "Series expansion of the integral at x -> inf". In particular, I have two divergent integrals and I am wondering whether their ratio is some finite number. Here it is: \left[\int_0^{\infty}...

Hello everybody, Is it possible that there can be an infinity A that is bigger than Infinity B ? How does this work/not work because i read that infinity is without limit(on wikipedia) so does saying one thing is bigger than another mean that a limit must be set to reach this conclusion or is...

If X is a locally compact Haussorff space, then the set of continuous functions of compact support form a normal vector space C_c(X) with the supremum norm, and the completion of this space is the space C_0(X) of functions vanishing at infinity, i.e. the space of functions f such that f can be...

Homework Statement Find limit x->0 (f(x))g(x). Here limit x->0 f(x) = 1 and limit x->0 g(x) = ∞Homework Equations I know that limit x->0 (1 + x)1/x = e ... (1) The Attempt at a Solution I have the answer which is elimit x->0 (f(x) - 1) * g(x) But I don't know how to proceed. I have to...

Can "infinity" be defined rigorously? In math, many of the most fundamental theorems and structures rely on the concept of an infinity. For example, we define the irrational (and transcendental) numbers as being the limits of some Cauchy sequence of rational numbers. This limiting process...

Both statements 1 and 2 are given as an explanation of why the original statement is true, but I don't understand why you can use statement 2 (since in the original vector equation you do not have Sin2(t), -Cos2(t)) Show why r(t) = <e-t, Sin(t), -Cos(t)> approaches a circle as t →∞. 1. As...

Homework Statement Determine constants c and C that do not depend on vector x but may depend on the dimension n of x, such that c ||x||_{∞} ≤ ||x||_{1} ≤ C||x||_{∞} Use this result and the definition of matrix norms to find k and K that don't depend on the entries of matrix A (but...

Dear all, I can not figure out why I got negative infinity in my output, so please help. Here is my calculation for FAMAX: FAMAG=SQRT(FX**2+FY**2+FZ**2) FAMAX=MAXVAL(FAMAG(1:NATOM)) and for FPBPMAX...

Homework Statement lim x→∞ ##\frac{7x^2 + x + 11}{4 - x}##Homework Equations The Attempt at a Solution I am sorry I am posting so much. But I think I have learned two different ways to compute limits at infinity of functions: one by the math lab tutor and another by the professor, but I am...

To those who have seen Toy Story please forgive title. This subject has I believe turned at least one mathematician mad, so I am hoping there are some maths people out there willing to take a chance. We need a starting point to get things moving either a line, a 2d surface or a 3d space as...

If both numbers approach 0 but one does not know their exact state, doesn't that mean the result can be either 1 or anything around it up to -∞and +∞? Does that in turn mean that 0/0 = Everything?

hi all, attached here is my code for 2d fdtd in polar coordinates, from 'numerical electromagnetic: the fdtd method (umran s inan, pg 94-96) written in fortran90. I have try a few approach I could think about to troubleshoot this code but the output is still infinity. Anybody here can give me...

In Srednicki's textbook (chpt 5) he has an expression: \int d^3k f(k) \int d^4x (\partial^2 e^{ikx}) \phi(x) and he wants to integrate by parts in order put the Laplacian on the field \int d^3k f(k) \int d^4x (e^{ikx})\partial^2 \phi(x) instead of the the exponential. He says that...

Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an...

Why does tangent go to infinity when it increases 0 to 90 degrees?

Why limit n--> infinity (3/4)^n = 0 Homework Statement Quick question. Brain flagrance. Homework Equations Why limit n--> infinity (3/4)^n = 0 The Attempt at a Solution ?? Why is this. How do you know.

Hi, I am trying to calculate second virial coefficient from interaction potentias and I have to Integrate at Infinity level and it seems that Integrate doesn't converge. can you help me integrate this function. Integrate is attached as an image. Regards Raymond

Homework Statement ##\int_{2}^{\infty} ue^{-u} du## The Attempt at a Solution What I did was find the family of functions described by the indefinite integral ##\int ue^{-u} du## then found the limit as b increases without bound. $$=\lim_{b\rightarrow \infty}...

I have just read a thread here:https://www.physicsforums.com/showthread.php?t=382031 Here is part from the thread. Please see the bold sentence in the quote. In this case, does it mean that my force(push) is larger than the push force from fixed charge. If so, how can I calculate the work that...

I have some problems finding Taylor's expansion at infinity of f(x) = \frac{x}{1+e^{\frac{1}{x}}} I tried to find Taylor's expansion at 0 of : g(u) = \frac{1}{u} \cdot \frac{1}{1+e^u} \hspace{10 mm} \mbox{ where } \hspace{10 mm} u = 1/x in order to then use the known expansion of...

ℂI am working on an assignment and have come across a question that I'm not quite sure how to approach. Here it is, with my "solution" and reasoning: "[F]ind the limit at ∞ of the given function, or explain why it does not exist. 24. h(z) = Arg z , z \neq 0" (Complex Variables Second...