Infinity Definition and 970 Threads

I've come across a snag in a proof, and I've become a little exasperated by the following limit: \displaystyle \lim_{p\to\infty} \biggl(\frac{{| d |}^{np+p-1} |x|^{p-1}}{(p-1)!} \{(|x| + |\alpha_1|) \ldots (|x| + |\alpha_n|) \}^p\biggr) I've tried the squeeze rule, but an upper bound...

Homework Statement find: lim(n\rightarrow\infty (1/n^2 + 2/n^2 + 3/n^2 + ... + n-1/n^2 ) Homework Equations [b]3. The Attempt at a Solution [/b I could guess that the limit is zero but i don't know howto prove it

Homework Statement limx->infinity (x+2)/(sqrt(81x^2+15)) Homework Equations The Attempt at a Solution The only thing i could think of doing was rationalizing the denominator to get (x+2)sqrt(81x^2+15) / 81X^2+15 however I am pretty sure this is the wrong route cause there doesn't...

question 1 : Prove that a sequence which is bounded above cannot tend to infinity What i did was state the definition ... but I'm trying to proof by contradiction. So i first suppose that a(n) tends to infinity , then a(n) > C . But since it is bounded above , C < or = to U , where U is the...

I'm studying for the GRE that's coming up in a week or two and I came across a problem where the answer given in the book does not make sense to me and I was wondering of someone here could explain it to me. Question: Lim as n goes to infinity of X_(n+1) / X_n Where X_n = n^n / n...

Is it true that 0.1% of the mass in an uncontrolled nuclear chain reaction gets converted into energy via E=Mc^2? And if this is so, then does the mass technically go to infinity in accordance with the Lorentz transformation before turning into energy?

The electron is traditionally considered a point particle with finite mass. Does this indicate that the electron might have near infinite mass density?

Find a value of constant "k" so a limit to infinity exists Homework Statement Find a value of the constant k such that the limit exists. Homework Equations lim x to infinity of x^3-6/x^k+3 The Attempt at a Solution I started by setting the equation equal to infinity and attempted to...

Homework Statement http://img254.imageshack.us/img254/121/77689018gc3.png Homework Equations A space is open iff there is for each x in A a ball (fully) contained within A. The Attempt at a Solution If I consider A in l^{\infty } then the sup =1. So for each x there is ball with a radius...

Homework Statement Hey guys. I tried solving these on my own, but I cannot seem to find out how to do this. 23. What are the steps to finding sqrt(3+6*x^2)/(2+5*x) as x goes to infinity? 41. Find the Horizontal Asymptotes for 17x/(x^4+1)^1/4 . I'm pretty sure its 17/1, but for...

Homework Statement Lim ((e^{2})-(\frac{t-3}{3}( * e^^{\frac{t}{3}}))) t -> -\infty [sorry for the formatting, I tried my best! that is "The limit as t approaches negative infinity of e squared minus (t-3/3) e to the t/3)]"] Homework Equations I am solving improper...

one raised to the infinity power help please! Let a and b be positive real numbers. For real number p define, f(p) = ((a^p + b^p)/2)^(1/p). Evaluate the limit of f(p) as p approaches 0. By directly plugging in zero, you would get (1)^inf. Wouldn't that equal 1 or would it be something else...

Homework Statement lim (SQRT (8x^3 + 5x + 10) ) / x^2 x -> infinity Homework Equations The Attempt at a Solution I tried factoring out x^3, but that didn't help anything.

Homework Statement A point charge of 2.0 10-9 C is located at the origin. How much work is required to bring a positive charge of 4.0 10-9 C from infinity to the location x = 30.0 cm? and it requests the answer in J Homework Equations W=-q2(delta)V DeltaV = Ke q1/d where...

\sum{a^ncos(nx)} from zero to infinity a is a real number -1 < a < 1 I rewrote this as a geometric series involving a complex exponential Real part of \sum{(ae^{ix})^n} Which is a geometric series with common ratio r < 1, so it converges to the sum (first term)/(1-r) which seems to be...

Homework Statement lim n -> infinity for (n!)^(1/n) Homework Equations The Attempt at a Solution hmm, i know that lim n approaches infinity, (n)^(1/n) will go to 1, but issit the same for n!?

Homework Statement Find the limit of each function (a) as x approaches infinity and (b) as x approaches negative infinity Homework Equations 1. g(x)=1/(2+(1/x)) 2. f(x)=(2x+3)/(5x+7) 3. h(x)=(9x^4+x)/(2x^4+5x^2-x+6) The Attempt at a Solution I don't know where to start.

This is for my intro physics 2 class Homework Statement Consider the charges Q at (-a, 0), -2Q at (0, 0) and Q at (a, 0). Such a combination of charges, with zero net charge and with zero net dipole moment, is called an electric quadrupole. a. Find the electric field along the x acis, for...

I need to make a power series in LaTex that looks like this u = \Sigma^{\infty}_{k=0} a_kx^k But I wan the infinity on top of the sum and the k=0 on the bottom like normal setting out but I can't find out how to do it? Hopefully someone from here can show me! Thanks

I resist posting as I have very little physics or math knowledge. I read quite a lot and would like to seek veiws on the following. Energy can't be created or destroyed. That implies it is eternal. If it is eternal it is infinite, at least in duration. Is it fair to say: Energy...

Hello, here is my question: if an object position can only tend to infinity, without ever reaching it (since infinity is just an abstraction), its image will tend to appear on the back focal plane of a converging lens, without ever forming there. The image will always be created on the image...

I have two questions about infinity: 1. Can infinity increase? In other words if a number can increase, wasn't it less than infinite before the increase? 2. If a number is finite, must it have a limit? The folks over in cosmology can't get through to me on how the universe can...

Homework Statement Hi all. Please take a look at this: \int_{ - \infty }^\infty {x \cdot \exp } \left( { - \left| x \right|} \right){\rm{d}}x = \left. {\left( { - \exp \left( { - \left| x \right|} \right) \cdot x} \right)} \right|_{ - \infty }^\infty + \int_{ - \infty }^\infty {\exp...

Why does the balloon analogy not accurately describe the universe? Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension. Astronomers seem unsure if the universe is finite or infinite. Physicists seem to...

Homework Statement Hi all. The wave equation at plus/minus infinity is zero: \left. {\left| {\psi (x,t)} \right| } \right|_{ - \infty }^\infty= 0 Does this also mean that: \left. {\left| {\psi (x,t)} \right|^2} \right|_{ - \infty }^\infty=0 ?

Lets imagine following: We have an infinite set of numbers representing the time. Now if we want to know how much time has spent in a specific sequence of this infinite set we see that this is impossible because there is infinite time passed before this sequence and infinite time passed...

Can anyone provide a visual of a Point at Infinity (or the ideal point)? I'm trying to visualize it and I apparently always end up interpreting every point on the Euclidean plane as an ideal point.

This may strike some people as really weird but after reading the book, God and the New Physics by Paul Davies, I came across a paragraph where he explains what happens at the singularity of a black hole. At the singularity, there is no concept of time apparently. So it is impossible to leave a...

What is 0/0. Any thing devided by 0 is infinity, 0 devided by something is 0 and anything devided by itself is 1.

I don't really understand why it hasn't been numerically added into modern math. I mean, we make all kinds of properties for zero, but we can't make properties for infinity? It gets messy from time to time, but we could define everything strictly so that it still works algebraically. Example...

Hello, Quick question. If space doesn't have, or consist of, an medium (ether?) would that mean space is infinitely small and large?

How does one define, given a complex function, the following: The function is analytic at infinity. The derivative of the function at infinity. It turns out that it's supposed to be quite common to define these terms, however I have never been shown either of them. I have a few...

Its looking quite simple problem but let me explain properly my question. Wave function as we know is also known as matter wave/field amplitude. Then definitely there is associated a wave with it. Then how can we say that wave amplitude vanished at infinite!

Homework Statement Define R^\infty_f = \{ (t^{(1}),t^{(2}), \ldots, ) |\; t^{(i}) \in \mathbb{R}\; \forall i, \; \exists k_0 \text{ such that } t^{(k})=0 \; \forall k\geq k_0 \} Define l^\infty = \{ (t^{(1}),t^{(2}), \ldots, ) |\; t^{(i}) \in \mathbb{R}\; \forall i, \; \sup_{k\geq 1} |...

Guys How do you think our reality would differ if the phi ratio were exactly 3 ? Is infinity a possibility? To me It must be, but in he same breath it can't be! "It is impossible to imagine an impossibility" By the way I am a retired Mechanical Engineer (Electricity power...

Homework Statement (3x-2) / (9x+7) As x approaches infinity. The Attempt at a Solution I know the procedure, but am then stuck: - Rearrange - Plug in infinity for x - Evaluate Tried breaking it into 3x / (9x+7) - 2 / (9x+7) The second thing would go to zero. The first, no...

"x = (e^(2kt) - 1)/(4e^(2kt) - 2)" How would I find the limit of this expression as t tends to infinity? As t --> infinity, the two exponentials also tend to infinity. However, that was as far as I could go. It is clear by subbing large values of t in, that the limit should be 1/4...

I heard somewhere that it is a matter of debate whether or not there is an absolutely highest temperature, analogous to absolute zero. This puzzled me because I thought that this is a direct consequence of Einstein's relativity: Temperature is average kinetic energy of a substance. But since...

Homework Statement I have done an integration and ended up with the result [-c/2 * [e^(-2x)]] |^infinity_0 = 1 The solution is that c=2 so that means to me that e^(2x) must turn into minus 1 for it to equal 1... but I'm not sure.. I've got graphcalc so I've been staring at the graph and...

I am interested in learning more about this concept where 1/0 can in this context be defined as infinity, however, I hear that infinity times 0 still will not reproduce 1 in this context. I have looked up some youtube mobius transformations and have read that "A Möbius transformation is a...

Homework Statement Evaluate lim (1+a/x)^x (that's limit as x tends to +infinity, sorry don't know how to latex that) Homework Equations The Attempt at a Solution Stumped. Having that x exponent has my confused. As x tends to infinity I know what's inside the brackets will tend to one, but the...

Hi all, I'm stuck on this problem, I can't solve it :confused: Sum(from 1 to infinity) of 8 / x^2(4+ln(x)) Does anybody have the fainest idea of how to solve? Thanks all

In ZF, the axiom of infinity says that the set of natural numbers exists. I was wondering if there was a (finitist?) weakening of ZF that included the axiom "the class of natural numbers exists".

[SOLVED] Voltage Query Homework Statement An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of + 150.0 \mu C uniformly distributed over its outer surface. Point a is at the center of the shell, point b is on the inner surface and point c is on...

Why does \lim(1+\frac{1}{x})^x = e x->\infty

Homework Statement \lim x-> \infty [x+1-ln(x+1)] Homework Equations The Attempt at a Solution How does one evaluate this? I don't know how to use L'Hopital's rule on this and I have infinity- infinity, which is indeterminate. Thanks!

I'm looking for help with my conceptual understanding of part of the following: 1) If a series is convergent it's nth term approaches 0 as n approaches infinity This makes perfect sense to me. 2) If the nth term of a series does not approach 0 as n approaches infinity, the series is...

Does any formula gives invalid results at infinity or zero compared to other values in the formula? I tried as an example some calculus at normal values gives answers and at infity and zeros the rule is broken... I think it is a must to formulate 0 with infinity and i don't know how...

Homework Statement 1) Find the cardnality of the set of constructible angles whose cosine is a) irrational b) rational 2. The attempt at a solution For the other questions I have posted my attempt, but for this one I really have no clue... Could someone please give me some general...

I am still struggling with the topic of cardinality, it would be nice if someone could help: 1) http://www.geocities.com/asdfasdf23135/absmath2.jpg In the solutions , they said that{y=ax+b|a,b E R} <-> R2. But I am wondering...what is the actual mapping that gives one-to-one...