Infinity Definition and 988 Threads

Homework Statement This problem is related to the system theory, using the H-infinity frame work to determine the maximum gain of a multivarible system. The system is described as G(s) = \begin{pmatrix} \frac{s}{s+1} & \frac{s}{s^2+s+1} \\ \frac{s-1}{s+2} & \frac{s-1}{s+1} \end{pmatrix}...

I'm trying to understand how the infinity norm of a transfer matrix is calculated. For example, assume a simple transfer matrix G(s) = \begin{pmatrix} \frac{s}{s+1} & \frac{s}{s^2+s+1} \\ \frac{s-1}{s+2} & \frac{s-1}{s+1} \end{pmatrix} Now, I'm trying to compute the \mathcal{H}_{\infty}...

**DISCLAIMER - I am super bad at LaTeX** Homework Statement Prove \lim_{x \rightarrow \infty}\frac{1}{1+x^2} = 0 Homework Equations I Think I proved it, but I feel like I'm missing something to make this a proof of ALL \epsilon>0 and not just one case. Maybe I did it right. I...

Suppose that a function f:R to (0,infinity) has the property that f(x) tends 0 as x tends to infinity. Prove that 1/f(x) tends to infinity as x tends to infinity. I don't really know where to start with this problem, I'm assuming it will involve some sort of epsilon proof but that's all I...

Suppose that the two functions f(x) and g(x) both tend to infinity then surely f(x) + g(x) also tends to infinity? How can you prove this though? Similarly f(x)*g(x) would also tend to infinity wouldn't it? f(x) - g(x) and f(x)/g(x) wouldn't tend to anything though surely since infinity minus...

What is the meaning of infinity?

Is there a finite model of ZF - Infinity?

Homework Statement Hi there, question asks "What is the difference between the sum to ten terms and the sum to infinity. a = sqroot 2 r = sqroot 2/2 The sum to ten terms, I worked out as 31 + 31 sqroot 2 The sum to infinity, I worked out as 2 sqroot 2 + 2 Homework Equations...

An object at the focal length distance from the lens is imaged at infinity,Do this mean that under this situation, our eyes could not see the image? but as our eyes could see the stars from infinity, do this mean that the image of lens which is discussed above is just viewed through screen ,and...

Hi,I have no idea on how to begin with this question.The question is: Prove that (n+a)!/(n+b)! ~ na-b as n goes to infinity.There are clue given that we can use Euler's limit and Stirling's formula to solve this question.Can you please give me some hints on how to start with this question...

Is there an actual infinitesimal in the way that there is an actual infinity. Or would zero fill that role.

http://arxiv.org/abs/0907.1090" :smile:

I'm currently reading a book, The Road To Reality by Roger Penrose, and trying to tackle some of the exercises in the process. My knowledge in mathematics is limited, but broad enough to complete some of the exercises. Anyway, one of them wants you to consider the one function...

Other than the Riemann Zeta function, what equation has a non-trivial infinity of zeroes with real part one-half?

lim n-> infinity of: (n^4 + n^2 + 1)^0.5 - n^2 -1 sin(2/n)/(1/n) (ln(n) + e^n)/(2^n + n^2) If anyone could explain the processes required to obtain the limits of any.. (or all) of these statements, that would be great

Try drawing this mentally: Start with a circle of radius r, draw n number of points spaced evenly on the circle. at each point on the circle draw another circle of radius r, once again with n number of points. What sort of a picture would one get repeating this process a million times, and as n...

hello i m a new user what is infinity minus infinity

I'm 16 and in high school. I've never taken physics or anything before. I have this equation that shows that pi = infinity times zero Ok. So if u take a circle with a diameter of 1 and draw equal spaced radius' and connect them you get a polygon with all equal sides. the more...

Homework Statement Hi all. We we look at z\rightarrow \infty, does this include both z=x for x \rightarrow \infty AND z=iy for y\rightarrow \infty? So, I guess what I am asking is, when z\rightarrow \infty, am I allowed to go to infinity from both the real and imaginary axis? If yes, then this...

Homework Statement lim (x-> infinity) sinh(x)sinh(e^(-x)) Homework Equations None really. The Attempt at a Solution L'Hospital?

Homework Statement lim_x->∞ of [√x + 2|x|] / [1 + x] Homework Equations lim_x->∞ of 1/[x^n] = 0 The Attempt at a Solution Hi everyone, Here's what I've done so far: I divided top and bottom by the highest power of x, i.e. x. So: [x^-1/2 +/- 2] / [1/x + 1] And taking...

Potential difference is what which makes sense. But calculating the potential difference b/w two points and one of them being infinity, where we define potential to be zero, we can actually find the potential at the point. Fine, agreed. Now, how do you define the potential at infinity to be...

Infinity can't be a constant because ∞ ± k = ∞ , but a constant changes (its) value when something is added or subtracted. But infinity can't be variable because the definition of variable is "A variable is a symbol that stands for a value that may vary" or stating in simple terms "In...

this isn't homework just wanted to know what the values are. tan -1 (infinity) = pi/2 tan-1 (0) = 0 what is sin -1 infinty and cos -1 infinity?

Is this true? n,m\in\mathbb{N} \lim_{n\to\infty}\sqrt[n]{\lim_{m\to\infty}\frac{1}{m}}=\lim_{n\to\infty}\lim_{m\to\infty}\sqrt[n]{\frac{1}{m}}=\lim_{u\to\infty}\sqrt[u]{\frac{1}{u}}=1 Thanks

Homework Statement X \geq Y > 0, find \lim_{n \to \infty} \left(\frac{2X^n + 7Y^n}{2}\right)^{1/n} Homework Equations The Attempt at a Solution I'm not really sure how to do it, but i guess I need to use the fact that \frac{Y}{X} \leq 1 , and so \lim_{n \to \infty}...

Sum of 1/ln(n)^(ln(n)) from n=3 to infinity? Does the sum of 1/ln(n)^(ln(n)) from n=3 to infinity converge or diverge? TNX ...

how do i find the limit for the following , where n->infinity 1/2 + 3/4 + 5/8 + 7/16 +9/32 +... i see that the numerator starts at 1 and has jumps of +2, giving me all the odd numbers the denominator starts at 2 with jumps of *2 giving all the powers of 2 so i have... + (2n-1)/2^n...

Hi all This is my first post so please be gentle with me! Limit of this rational function as x approaches infinity? f(x) = (x^3 - 2x)/(2x^2 - 10) I was under the impression that if the degree of the polynomial of the numerator exceed that of the denominator then there could be no...

Homework Statement Evaluate the integral. http://www.freeimagehosting.net/uploads/176e17ca2f.jpg Homework Equations http://www.freeimagehosting.net/uploads/3168397520.jpg The Attempt at a Solution http://www.freeimagehosting.net/uploads/3168397520.jpg I am stuck here as the book...

Homework Statement Evaluate the integral. http://www.freeimagehosting.net/uploads/176e17ca2f.jpg Homework Equations The Attempt at a Solution

why is it that we can use the residue at infinity on the methods of contour integration example on wikipedia for the last one? we can only use the residue at infinity when it is a rational function, i.e. the ratio of two polynomials, if I'm wrong when i say this, why?

I was reading the wiki on this and found it very interesting and would like to hear what established mathematicians and physicists think about this kind of philosophy. Personally I believe that God(used in reference to the universe itself, am not religious) created infinity and man created...

Let me first say I am in high school and don't understand very much calculus or advanced physics. But through my independent work i have created a theory in which i personally can not find any flaws with. I would ask for constructive critisms on this theory. thanks! It is my understanding...

I need to find the limit x -> infinity of the following: y = x ( (2x/a) / (1 + (2x/a)) ) Simplifying.. y = x ( (2x/a) / ((a + 2x)/a) ) y = x ( 2x / (a + 2x) ) y = 2x^2 / (a + 2x) Is this even right in the first place? because I have no idea how to evaluate the lim x -> infinity.

limit as X--> infinity of cos(x) Homework Statement Find the limit. \stackrel{lim}{x\rightarrow\infty}cos(x) The Attempt at a Solution As best as I can tell by putting larger and larger numbers in my calculator, there is no limit, as cos(x) just oscillates between (-1,1). So is the...

Homework Statement Find the limit as x approaches infinity of (sqrt(1+3x^2))/x The Attempt at a Solution I tried using l'hopital's rule, but it gave me 3x/(sqrt(1+3x^2)) which doesn't help me at all.

so i understand how to resolve a limit at x->oo, but from a conceptual standpoint, i do not get it. for example, limit x->oo, 4x/5x so the answer is 4/5, but oo/oo is an indeterminate expression i understand that if i treat x as a variable, then it makes sense, but still if the example was...

Homework Statement integral [from e to infinity of ] 67 / (x(ln(x))^3) read as the integral from e to infinity of 67 divided by x times cubed lnx. Homework Equations The Attempt at a Solution i know it converges, but i got the value 67/2

Homework Statement \sum(\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})}k as k \rightarrow\infty Homework Equations Root test: (ak)1/k The Attempt at a Solution (ak)1/k = (\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2}) does it equal 0? since 1/\infty = 0 but its \infty - \infty i would have to...

1. My problem is such: Find the limit of \lim_{x \rightarrow \infty} \sqrt{9x^2+x} -3x 2. No relevant equations 3. I multiplied \frac{\sqrt{9x^2+x} -3x}{1} * \frac{\sqrt{9x^2+x} +3x}{\sqrt{9x^2+x} +3x} = \frac{x}{\sqrt{9x^2+x} +3x} I am now quite confused as to where to go...

Homework Statement \lim_{x \to -\infty} x + \sqrt{x^2 + 6x} Homework Equations The Attempt at a Solution Previous attempt was guessing it was \infty, but I see now my flaw and the actual answer is -3. Somewhere else on the web, might have been this forum, it was said that one could flip the...

Homework Statement I have a space M which is a sequeces of real numbers \{x_n\} where \sum_{n = 1}^{\infty} x_{n}^2 < \infty How can a series mentioned above be become than less than infinity?? Please explain :confused: Sincerely Cauchy

Finding lim f(x) as x-->+/- infinity? f(x)= x^(5/3)-5x^(2/3) Need to find limit f(x) as x-->+infinity, and x-->-infinity?

Suppose we have the following shape in the complex plane: The EXTERIOR of the semi-infinite strip bounded by 0 < y < 1 and x > 0. The two physical angles making up the rectangle have interior angles of 3*pi/2 and thus exterior angles of -pi/2. Now, because the sum of the exterior angles of a...

I cannot remember if infinity is an upper bound for a subset of R? I think so, but I want to be sure before I use it in a proof.

Homework Statement Prove that lim n \rightarrow\infty 2^{}n/n! = 0 Homework Equations This implies that 2^{}n/n! is a null sequence and so therefore this must hold: (\forall E >0)(\existsN E N^{}+)(\foralln E N^{}+)[(n > N) \Rightarrow (|a_{}n| < E) The Attempt at a Solution...

Homework Statement What is the limit as x goes to positive infinity of: (4x2+3x+8)/(6x2+5x-7)? Homework Equations The Attempt at a Solution Usually I would factor the top and bottom and see if something cancels, but that doesn't work here. Also l'hopital rule doesn't work...

Homework Statement For the following function decide whether f(x) tends to a limit as x tends to infinity. If the limit exists find it. Homework Equations f(x)=[xsinx]/[x^2 +1] The Attempt at a Solution I thought about using L'Hopitals rule, so i got: [sinx + xcosx]/[2x]...

In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12 and 3-13, the bookkeeper measure of radial velocity (i.e. radial velocity as measured from infinity) is derived. Basically the equation for 'Energy in Schwarzschild geometry' is established-...