Limit Definition and 999 Threads

Hi, can anybody help me with this two limits? I have to prove them by the definition of limit. Thank you in advance.

How do you solve this kind of limit? \lim_{x \to ∞} \left( \frac{x^2 - 1}{x^2 + 2x + 5} \right)^{-2x} Please give me a clue.

I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.2: Topological Spaces ... I need help in order to fully understand Singh's proof of Theorem 1.3.7 ... (using only the definitions and results Singh has established to...

(NOTE: I have had a few similar postings lately on this subject, but they were much broader in scope, so I am posting only for this particular case; everything else has been figured out.) If given that limx -> a f( x ) = +∞ limx -> a g( x ) = +∞ what is the epsilon-delta formulation for...

What is exactly the definition of symmetric limit? It's the first place in the book that I see this notation, and they don't even define what it means. How does it a differ from a simple limit or asymptotic limit? I found a few hits in google, but it doesn't seem to help...

I’ve read many Legends and Canon Star Wars books and I always take away stuff on their limits of technology and science. Over the years; here are some things they said science can’t do. 1.) Cybernetic liver- In Lost Stars, it was said Ciena’s liver could not be replaced as it was one of the...

I have the function: ##\sqrt{\left(\frac{x}{h}+1\right)^{2}+\left(\frac{y}{h}\right)^{2}}-\sqrt{\left(\frac{x}{h}\right)^{2}+\left(\frac{y}{h}\right)^{2}}## I would like to find an analytical solution, the equivalent function, in the limit of h approaching zero.Additional info which might be...

A 2019 paper by Gorecki et al. derives an uncertainty principle limit that is larger than the conventional Heisenberg limit by a factor of ##\pi##: https://arxiv.org/abs/1907.05428 I'm wondering if any QM experts have seen this and what your thoughts are.

Hello all, Given following limits: ##\lim_{x \rightarrow 1} {\frac {\sqrt x -1} {x^2 - 1}}## ##\lim_{x \rightarrow 1} {\frac {\sqrt {x+1} - 2} {x - 3}}## ##\lim_{x \rightarrow 1} {\frac {\sqrt[3] x - \sqrt[4] x} {\sqrt[6] x - \sqrt x}}## Those limits can be evaluated by letting ##x = t^2##...

How can i get rid of the last delta x

Someone asked me what a dime was (this is UK.) I, not knowing, nevertheless promptly replied, it must be 5 cents, because they called their 55mph speed limit the double dime. Then of course went to Google to check and found that it is 10 cents. How does double 10 become 55? So back to Google...

Hey! :o I want to check the existence of the limit $\lim_{x\to 0}\frac{x}{x} $ using the definition. For that do we use the epsilon delta definition? If yes, I have done the following: Let $\epsilon>0$. We want to show that there is a $\delta>0$ s.t. if $0<|x-0|<\delta$ then...

An object or force cannot have a constant acceleration for an infinite time. (this is an axiom of motion). If an object or force could have an infinite constant acceleration, then it would eventually be infinitely faster than the speed of light. Thus, a force has a limit, The Barlow Limit.The...

Let be I(a,b)f(x)dx the integral from a to b of the function f(x) if we made the change x=(b-a)t+(b+a)/2N the integral transforms into I(-1/N,1/N)f((b-a)t+(b+a)/2N)dt(b-a) and after that taking the limit N tends to infinite and knowing that in that case 1/N tends to 0 we could say that the...

I have been seriously thinking and wondering about the existence of any limit whatsoever of our universe.Is there such thing? And if there is - What would it be?Is there anything behind that border ? And if there is nothing behind it - Where are we located ?Is there any limit to this unkown...

Does Max Plancks E=hv imply there is a minimum energy that a photon can have?Are all photons just bunchs of these minimun energy photons?

is 0^0 1?cloud strife

why is it that in the theory of relativity the speed of light or other electromagnetic radiations is taken as the highest?We dance round in a ring and suppose,but the secret sits in the middle and knows.- Robert Frost

When einstien theorized that the speed of light was the limit to velocity he overlooked the fact that two bodies traveling in opposite directions at near the speed of light would be at almost double the speed of light relative to each other... So I say if you want to exceed the speed of light...

Is heat, or temperature, discretely quantized or is it possible to have an infinately small gradient? For example can an atom absorb or radiate 1/ joules of thermal energy or is there a limit, such as plank's constant, that only allows discrete quantities of thermal energy to be exchanged?I'm...

I have evolved into a computer. I can isolate errors in every theory known to man, including the theory of relativity. I have used binary logic to understand motion at the point particle level. Theory is a waste of time, the human female goes into heat.I am the universe.lp

How many consecutive questions can one ask a great physicist until she cannot provide a scientific answer? (Those of you with two-year olds or Turing machines will appreciate this).For instance:Q1. Why is the Sun round?A1. Because of the symmetric gravity acting upon it in gaseous state.Q2. Why...

this is for all those math geniuses!!if the limit of [f(x)+g(x)] = 6 as x approaches 1and the limit of f(x) * g(x) = 4 as x approaches 1then determine limit as x approaches 1 [f(x)-g(x)]^2i tried manipulating the first two equations for f(x) and then making them each equal each other to solve...

In restarting this thread I ask all those who reply to please refrain from "cutting" down other people's opinions, and to refrain from straying too far off-topic. Thanks!Ok, If the Planck length is (roughly) the shortest distance in the universe, then that PROVES the runner HAS to stop once he...

How do I calculate the limit for these:2^n / 3 ^nand5n / ( n^.5 + 1 ) when n --> infinitymrzero

Is there an expression (for example 2+x) for which a limit for a certain value exist (for example lim[x->1] 2+x = 3), but there is currently no easy way to find it (we must use the tedious substitution method: ie x=0.9, x=0.99, x=1.1, x=1.01, etc)?

The theory of relativity states that you cannot go over the speed of light.The spped of light is lower in different media for example water.Does this mean that the speed limit in water is less than that in a vacuum?"All Science is Physics or stamp collecting" - Rutherford , I think

lim...........h - 8h -> 8 cube root (h) - 2In words: I am looking fot the limit, as h tends to 8, of (h - 8) divided by the (third root of x) -2.

186,000 miles per second in a vacuum. Heisenberg tells us, in a 'round about way, that there is no 'vacuum'. It (the vacuum of space) is filled with virtual particles, fields . . . all sorts of minimum energy stuff. Can light ever reach it's ultimate speed of 186,000 m/s, if there is no true...

Why isLim [ f(-2) � f(h � 2) ] /h = -f� (-2), when h --> 0Why � -f � ??The limit exists.mrzero::nrzero.com

Whats the amount of energy allowed at this scale?How much energy can be present without streching space beyound this limit our time?

I am asked to find the limit superior and inferior of [ 1 + (-1)n] n ( 1 +1/n). Clearly it seems as though the limit superior should be oo, but I wonder if that is semantically o.k. or if the answer should be "undefined" or something.------------------------------"I want my tail back"-Grady...

I dont really know if I'm right.pin point particle theory,I think,is that matter can be divided infinity by cutting a piece into two then taking one and doing it again,trying to find how far you can go until you find the last possible indivisable piece of mass.I was thinking if you looked at it...

Everyone says that light has no mass but has momentum and energy, so why shouldn't something have no mass travel at infinite speed because if something has no mass, infinite energy will not be needed to accelerate it. So why is speed of light an universal limit of speed?

I am curious of the range of our senses. I think it's important we know the small part of reality that our senses allow us to see, smell, hear, feel and taste. II've heard that people who get surgery on their eyes can see UV light and have seen the small range of light we see on the EM...

you can have two objects moving away from each other at 51% of the speed of light, this meaning object 1 relative to object 2 is going faster then the speed of light away from each other but that�s cheating with the point of view on beating the speed limit so what is the universal speed limit...

(Reposted). A gravitational black hole abhors a "naked" singularity, but allows it the observable property of charge with E-M field. Similarly, the horizon for "electronic black holes" limits what we may eventually know about the electromagnetic structure of a charged particle.An electronic...

I don't know whether I'm doing this correctly but the textbook says:"Sketch the graph of any function that satisfies the given conditions in each case."I tried this one for example:f(x) = 1, if x < 1 and lim f(x) = 2..............................x->1+This is how I sketched...

I know this isn't a math forum but since you people have helped me out in the past I hope you can again :)I've been burning my brain over this question:"If limx->3|f(x)|=1, does the limit limx->3f(x) have to exist? If so, what is it?What if limx->3|f(x)|=0 ?"I think that limx->3f(x) would have...

I have taken the basic physics classes, and have no problem understanding the repurcusions of SR (mass increases at speed, time slows, distance increases, etc.), but I don't know _how_ Einstein came to the conclusion that light was the speed limit. All I was taught, was that he had an epiphany...

evaluate the following limitlim [x^(1/2) - 8] / [x^(1/3) - 4] , when x--> 64

Poll Question:Why do we have light speed as the max limit for speed?Choices: Don't know. Einstein said, so! I figured that out. good question.

I need to know the equation to find Chandraskar's limit. ( the equation that says if a star will blow or collapse) Thanks, for any help."I can't believe in a god that has to be praised all the time."-Nietzsche

Hi,Here is a limits problemlim { tan^ -1 x + sin ^-1 x }/ sin^3 xx->0tan^-1 x and sin^-1 x mean inverse functions.By the way can anybody tell me how to put numbers as superscripts or subscripts.

I need an example of a limit used to find the area under a curve, not just x-->0. I would like a numerical example._____________________"When you get into college, biology takes brains, physics takes work, and calculus takes up the whole page" -Me

If the planck length is the smallest possible size for any particle to be, this means there is a limit to how small things can get. There is no infinite regress of size. Is the same true then, for time? When we talk about planck time, does this mean the shortest possible measurement of time? If...

When does an on/off ratio become impractical? I've read that typical CMOS devices have an on/off ratio of 10^6-10^10. Is there a lower limit that prevents logic devices from functioning appropriately? As in, what is a practical lower limit for the on/off ratio but still enable logic functionality?

I wanted to know what is understood as the dispersive approximation (or limit) in the context of the Jaynes-Cummings model for one mode of the field.

$$\lim_{x\to\infty} (x^3+x^2 +\frac{x}{2})-x^3\sqrt{(1-\frac{1}{x^6})} = \lim_{x\to\infty} x^3+x^2+ \frac{x}{2} -x^3=\lim_{x\to\infty} x^2 + \frac{x}{2} = \infty. $$ is this it?

Would this ##f'(x)>g'(x)\,\forall x\in [a,\infty)\text{ and }f,\,g\underset{\infty}{\to}0\Rightarrow \lim_{x\to\infty}f(x)/g(x)=0## hold if ##\frac{f(x)}{g(x)}\neq c##?