Infinity Definition and 970 Threads

I found a torrent online of Apostol's "Mathematical Analysis" 1st edition and I think I found a typo, or whoever scanned the book cut off the edge a bit... Apostol writes that the extended real number system R* is denoted by [-∞, +∞] while the regular real number system R is denoted by (-∞...

Homework Statement Prove that if limXn = +∞ and limYn>0 then limXnYn=+∞ The Attempt at a Solution limXnYn = limXnlimYn = (c)(+∞) where c is a positive real number I know in my head that a positive number multiplied by infinity is positive, but I am unsure how to prove this and we have...

i wonder about this proof for l'hopital for infinity over infinity: http://planetmath.org/encyclopedia/ProofOfLHopitalsRuleForInftyinftyForm.html how is this proved: http://bildr.no/view/1011658

Hi, I'm not sure if this is the right section, but I'm talking about numbers :). The questions is as written in the title: Is a number preceding infinity, finite?

Simple question just as the title says, but I can't remember or derive the solution for the life of me. I know that the answer is 0. I know why the answer is 0. But I need to know the mathematical derivation of the solution, and that's the part that I can't remember. So, to reiterate, how do you...

Lim x→∞ \frac{7x^2-14x+7}{\sqrt{2x^4-4x^3+x+7}} Normally wouldn't have an issue here, just slightly confused by the sqrt. Attempted solution: \frac{7x^2-14x+7}{\sqrt{2x^4-4x^3+x+7}}*\frac{x^-2}{x^-2} Yields \frac{7}{\sqrt{2}} Is this correct? Similarly: lim...

Hi I was wondering about the meaning of the infinity norm || x ||_\inf= max\{|x_1|, |x_2|...|x_n| \} if a norm is a function that assigns a strictly positive length or size to all vectors in a vector space, why do we assign the maximum (or sup) as the value of this norm ? It must be a...

Homework Statement Hello everyone, I am just new to this forum and also a beginner at calculus. I have a question from my textbook. It's: Find an example of f(x) that satisfies the following conditions : f(x) is differentiable for all x>0; limx->∞f(x) =2; limx->∞f'(x) does not exist...

I'm currently trying to reassess my image of the BB and the universe in general. I've been led to believe/understand that at the moment after the creation event the universe would fit millions of times within the space occupied by a single subatomic particle. However there's something wrong...

Homework Statement Find the vertical asymptote(n) and evaluate the limit as x \rightarrow n^-, x\rightarrow n^+, or state Does Not Exist. Homework Equations \frac{\sqrt{4x^2+2x+10}-4}{x-1} The Attempt at a Solution I have taken the limits at \pm\infty=2,-2 and understand those are my...

I am aware that Bessel functions of any order p are zero in the limit where x approaches infinity. From the formula of Bessel functions, I can't see why this is. The formula is: J_p\left(x\right)=\sum_{n=0}^{\infty}...

Hi , I have been thinking of this question for a long time. Can someone give me an advice? There are three known matrices M, N, and K. M is a (4*4) matrix: M= [ 1 0 2 3; 2 1 3 5; 4 1 1 2; 0 3 4 3 ] N is a (4*3) matrix: N= [ 3 0 4; 1 5 2; 7 1 3; 2 2 1 ] K is a...

Homework Statement Q.: The numbers \frac{1}{t}, \frac{1}{t - 1}, \frac{1}{t + 2} are the first, second and third terms of a geometric sequence. Find (i) the value of t, (ii) the sum to infinity of the series. Homework Equations S\infty = \frac{a}{1 - r} The Attempt at a...

"Infinity" at the Center of the Galaxy http://www.sciencedaily.com/releases/2011/07/110719151234.htm http://www.wired.com/wiredscience/2011/07/milky-way-ribbon/ New observations from the Herschel Space Observatory show a bizarre, twisted ring of dense gas at the center of our Milky Way...

Homework Statement Q.: A geometric series has first term 1 and common ratio \frac{1}{2}sin2\theta. Find the sum of the first 10 terms when \theta = \frac{\pi}{4}, giving your answer in the form h - \frac{1}{2^k}, where h, k \in N. Homework Equations Sn = \frac{a(1 - r^n)}{1 - r}, when...

Homework Statement Q. Find the range of values of x for which the sum to infinity exists for each of these series: (i) 1 + \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + ... (ii) \frac{1}{3} + \frac{2x}{9} + \frac{4x^2}{27} + \frac{8x^3}{81} + ... Homework Equations S\infty =...

Homework Statement Q. Find, in terms of x, the sum to infinity of the series... 1 + (\frac{2x}{x + 1}) + (\frac{2x}{x + 1})^2 + ... Homework Equations S\infty = \frac{a}{1 - r} The Attempt at a Solution S\infty = \frac{a}{1 - r} a = 1 r = U2/ U1 = (\frac{2x}{x + 1})/ 1...

Homework Statement \sum_1^\infty \frac{n^2}{n!} = The Attempt at a Solution Context: practice Math GRE question I don't know how to answer. Well, it's bigger than e and converges by the ratio test. Adding up the first 5 or 6 terms suggests that it converges to 2e. That's good enough for a...

Homework Statement Q.: A geometric series has first term a and common ratio r. Its sum to infinity is 12. The sum to infinity of the squares of the terms of this geometric series is 48. Find the values of a and r. Ans.: From textbook: a = 6, r = 1/ 2 Homework Equations...

Homework Statement So I'm trying to evaluate the following integral: 4\pi r^2{\int_0}^\infty r^2\frac{\sin{sr}}{sr}dr which after canceling out one of the r's, gives an integral similar to that of xsinx. I need to show that this integral vanishes for all values of s that are not 0...

Homework Statement Consider the equation \dot{x} = rx + x^3, where r>0 is fixed. Show that x(t) \rightarrow \pm \infty in finite time, starting from any initial condition x_{0} \neq 0. Homework Equations I can think of none. The Attempt at a Solution The idea alone of x(t) approaching...

If the odds of getting the right answer are one in an infinity, is it possible to stumble on to the right answer?

Homework Statement if lim f(n) = s , prove that lim (f(n))^{1/3} = s^{1/3}. How do you know that as n approaches infinity, f(n) and s have the same sign. n is just an index in this case and f is not a function but a sequence. The attempt at a solution so we know that |f(n) - s| < epsilon...

Homework Statement Hi, I have just now come to the realization that tan(pi/2) is not infinity but complex infinity. I was wondering why and can't seem to find the answer. I was told all through high school that tan(pi/2)=infinity or undefined but not complex infinity. Homework Equations The...

Is it true, that there is an infinite amount of numbers between 0-1? Think about it, what number comes after 0, and before 1? Whenever I try to think about it, my mind goes blank. Discuss.

given (-1)! = \tilde{\infty} , which is complex infinity the real part of \tilde{\infty} is \overline{?} which is "a quantity whose magnitude cannot be determined" as stated in wolfram's site at http://functions.wolfram.com/Constants/ComplexInfinity/introductions/Symbols/ShowAll.html"...

Homework Statement Prove that lim(x->infinity):x[1/x] = 0 by epsilon-delta defintion. (WITHOUT USING THE SQUEEZE THEOREM) The Attempt at a Solution well, It's easy to prove that x[1/x] approaches 0 as x goes to infinity using the squeeze theorem, but the question is to prove that without...

Homework Statement In Griffiths' Introduction to Quantum Mechanics problem 2.22 as well as 6.7, I used substitution to complete an integral. The original integral had limits from negative infinity to positive infinity. For my substitution, I had a complex constant term added to the original...

This is a problem related to julia sets but its more of a mathematical problem so I posted it here. x= x^2 - 2 For what values the iteration does not go to infinity. I can't figure out how to calculate that. I tried calculating a nth term of this in terns of initial term but all in vain.

Homework Statement How would you take this limit? The function is: lim_{x\rightarrow -∞}\frac{\sqrt{9x^{6}-x}}{x^{3}+1} Homework Equations The Attempt at a Solution Uh, square root of negative infinity? Graphing tells me that this should go to -3. I just recalled that I can...

Homework Statement The problem is to prove that the limit of sin(sqrt(x+1)) - sin(sqrt(x-1)) when x goes to infinity doesn't exist. The Attempt at a Solution well, I converted sin(sqrt(x+1)) - sin(sqrt(x-1)) into the alternative form -2sin(sqrt(x+1)/2 -...

Homework Statement The problem is to prove that the limit of [x]+[-x] at infinity does not exist. The Attempt at a Solution I used the argument that the function [x]+[-x] is equivalent to the function f such that it gives 0 for all integers and gives -1 otherwise. therefore because the...

Could I write down all the real numbers from zero to 1? I know this sounds crazy. But let's say I have a person for every number between 0 and 1 . and then I tell them to write down a number different from every one else. Suppose they have the largest infinite amount of time to do this...

If we have an exponential fuction, (for example) Limx->∞ e(x2+2x+1)/(x2-3) Would we first determine the limit of the "argument" (not sure if right word) of ex and then replace the "argument" with the limit and then evaluate it? So for the example above, The limit of...

I'm having a hard time learning from the textbook, I know I can do this if someone just outlines what my goal is here... and what I can interpret from that goal. The solutions handbook just makes seemingly random algebraic changes to the limit function and then tells me what the answer is...

Does the following make sense: E(e^{-X}) = 0 \Rightarrow X = \infty\quad a.s. ? (Intuitively yes, but mathematically?) Thank you in advance for your help! :-) /O

Homework Statement This is a problem I came up with when I was doing something similar in Spivak's Calculus; although a simpler version. Suppose, we have f(x)=x^3 and g(x)=x^2 find \lim_{x\rightarrow \infty} f(x)/g(x) Homework Equations N/A The Attempt at a Solution...

Hello, I have a question. How do you design a buffered band pass filter with a resistive load of infinity? I have a feeling that a resistor with a resistance of infinity is an open circuit. Although how can this be implemented in a type of filter seen in the attachment? Thank you.

I have to minimize an expression of the following type: min <a,x>-L||x-u||_inf^2 s.t.: ||x||_inf <= R, where a is a vector of coefficients, x is the vector of decision variables, <.,.> denotes the scalar product, R and L are scalars, u is some constant (known) vector, and 'inf' denotes...

Please teach me this: What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms. Thank you very much in advanced.

Homework Statement Suppose that f and f' are continuous functions on \mathbb{R}, and that \displaystyle\lim_{x\to\infty}f(x) and \displaystyle\lim_{x\to\infty}f'(x) exist. Show that \displaystyle\lim_{x\to\infty}f'(x) = 0. Homework Equations Definition of derivative: f'(x) =...

does pi over infinity equal .00000...314159...? if not please post opinions. :(

Homework Statement [PLAIN]http://admitere.ncit.pub.ro/moodle/filter/tex/pix.php/5c2cef253f2db3240db03f8c9b6c9463.gif lim n->infinity of a[n] = ? Homework Equations |x| > 1The Attempt at a Solution Well, actually i figured out that the sequence converges, and I've tried to solve it using...

If we headed directly into space traveling at many times the speed of light (ignoring for a moment that you can't travel that fast), maintaining exactly the same course for the whole trip, would or could we eventually find ourselves heading back to Earth? I got a reply elsewhere, suggesting I...

I'm interested in philosophers' opinions on a question that I posed in another forum (https://www.physicsforums.com/showthread.php?t=496119). As I say in my latest post, the entire thread was sparked by the comments of the Philosopher of Chemistry, Joachim Schummer: We have no reason at...

Homework Statement This is the solution to an IVP, and the question asks how the function behaves as x Approaches infinity...

Homework Statement integrate (x*2e^x)/(2e^x-1)2 from x=0 to infinity Homework Equations The Attempt at a Solution let t=2e^x-1 => x=ln((t+1)/2) dt = 2e^x dx Thus equation is now integrate (ln((t+1)/2))/t^2 dt from t=1 to infinity Then let u = (t+1)/2 => 2du=dt Equation now...

Hello. The word "infinity" often comes up in physics, but observational evidence seems to preclude any form of infinity whatsoever: either everything must be infinite, or nothing can be infinite. My line of thought comes from the fact that the density of our universe is not infinite. Therefore...

I have been advised that the questions that I ask in another thread in the Chemistry Forum may be better assessed by those who frequent the General Physics Forum. I would be much obliged if you could take a look at the following link, and provide any thoughts, feedback, ideas that you may...

If this is the wrong place for these sorts of musings, I greatly apologize and I would be profoundly obliged if someone could point me in the right direction. Otherwise, on with the question. I have repeatedly heard it said that the number of chemical species and, by extension, the...