Limit Definition and 999 Threads

Homework Statement Can I use L'Hopital's rule here. What I get as a solution is -30/-27 while in the notebook, without using the L'Hopital's rule the answer is -(2/27) The attempt at a solution The derivatives i get are: x/(x2+5)½ (3x2+2x)/3(x3+x2+15)⅓ 2x-5 ½ and ⅓ are there because it's...

Hello PF, I am searching for a proof that I couldn't find on the internet. Theorem: E in X a metric space. p in E. p is an interior point of E if and only if p is not a limit point of (E complement)' Sorry for notations but I have no idea how to insert Latex here.

Dear Everybody, I am having trouble to determine the value of delta when c is strictly greater than 0. Here is the work: The Problem: Find the Limit or prove that the limit DNE. $\lim_{{x}\to{c}}\sqrt{x} for c\ge0$ Proof: Case I: if c>0. Let $\varepsilon>0$ Then there exists $\delta>0$...

The problem In this problem I am supposed to show that the following series converges by somehow comparing it to ## \frac{1}{k\sqrt{k}} ## : $$ \sum^{\infty}_{k=1} \left( \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} \right) $$ The attempt ## \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} =...

1. Homework Statement Question attached. I am looking at the second line limit ##\beta (h/2\pi) \omega << 1 ## 2. Homework Equations above 3. The Attempt at a Solution Q1)In general in an expansion we neglect terms when we expand about some the variable taking small values of the...

Is anyone aware of any theory which includes a theoretical limit on acceleration in the same way C is the universal speed limit? [[By this I do not mean some sort of practical limit set by energy density and known systems of propulsion.]]

The quotient limit laws says that the limit of a quotient is equal to the quotient of the limits. If we had a limit as x approaches 0 of 2x/x we can find the value of that limit to be 2 by canceling out the x’s. If we split it up we get the limit as x approaches 2 of 2x divided by the limit...

I am studyng accretion process on "Astrophysics in a nutshell" by Dan Maoz and I have some doubts about the derivation of the formula for the eddington limit. I understand what the edding limit is. The accretion rate cannot be arbitrarly large. The starting point is to consider an electron at a...

Hello, I'm supposed to calculate the limit of this: $$\lim_{{x}\to{1}}\left(\frac{x}{x-1}-\frac{1}{\ln x}\right)$$ Combining the fractions: $$ \frac{x}{x-1}-\frac{1}{\ln x} = \frac{x\ln x-x+1}{(x-1)\ln x} $$ The substitute $$ u=x-1 \implies x=1+u $$ then gives...

Is there a gravitational variant of the Schwinger limit? I mean: a strong gravitational field can separate virtual dipoles with tidal forces. The force applied to the positron is different from that applied to the electron (though both are attractive) and, if this difference is high enough, the...

Homework Statement From here, question C. http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx lim (x,y) -> (0,0) \frac {x^2y^2}{x^4 + 3y^4} Homework EquationsThe Attempt at a Solution So if we approach along the x axis, we know y will be 0, so we get lim (x,0) -> (0,0) \frac...

From Rosenlicht, Introduction to Analysis: Definition: Let E, E′ be metric spaces, let p0 be a cluster point of E, and let f(complement(p0)) be a function. A point q ∈ E" is called a limit of f at p0 if, given any e > 0, there exists a δ > 0 such that if p ∈ E , p < > p0 and d( p, p0) < δ...

Homework Statement ##\lim_{h \to 0} \frac{f(x - 2h) - f(x + h)}{g(x + 3h) - g(x-h)}## While f(x) = cos x g(x) = sin x Homework EquationsThe Attempt at a Solution Using L Hopital i couldn't make it more simple. I tried to divide it by cos and sin Can you give me clue?

Homework Statement : Find [/B] limx->∞(xα(sin2x!)/(x+1) α∈(0,1) Options are: a)0 b)1 c)inifinity d)does not existHomework Equations : -[/B]The Attempt at a Solution : limx->∞(xαsin2x!)/(x+1)[/B] Dividing the numerator and denominator by xα, we have:limx->∞sin2x!)/(x1-α+x-α) clearly x−αis tending...

Homework Statement :[/B] limx->0xsin(1/x)Homework Equations : [/B]-The Attempt at a Solution :[/B] I feel the limit does not exist. Because sin(1/x) is largely changing value as x approaches 0,(since it is an oscillating function), and in limit, we check what happens in neighborhood of the point...

Homework Statement Let ##x_1=1## and ##\displaystyle x_{n+1} = 3 x_n^2## for ##n \ge 1##. a) Show if ##a = \lim x_n##, then ##a = 1/3## or ##a = 0##. b) Does ##\lim x_n## actually exist? Homework EquationsThe Attempt at a Solution I have proven before that, in general, ##\lim s_{n+1} = \lim...

My teacher says I have to solve all the limits at once, but I don't understand why it is mathematically incorrect to solve one limit before the other. The test is here:

Homework Statement Find and prove ##\operatorname{lim} \frac {1}{n^2}##. Homework Equations In the textbook, we assume that the limit is going to infinity without writing it. If L is the limit, we have for all ##\epsilon > 0##, there exists ##N## such that ##n \epsilon \mathbb{Z}## and ##n >...

For the last 88 years we have used Subrahmanyan Chandrasekhar's calculations to determine the maximum mass of a white dwarf. As a result of that calculated mass limit, a peak brightness was derived and the Standard Candle was born. However, those calculations were made based upon certain...

Homework Statement Finding the value of the limit: $$\lim_{t\to +\infty} t+\frac{1-\sqrt{1+a^2t^2}}{a}$$ ##a## is just a costant The Attempt at a Solution At first sight I had thought that the limit was ##\infty## but then I realized that there is an indeterminate form ##\infty - \infty##. I...

Homework Statement Show that the sequence of partial sums s_{n} = 1+\sum_{i=1}^{n} \left(\prod_{k=1}^{i}\left( \frac{1}{2} + \frac{1}{k}\right)\right) converges, with n\in \mathbb{N}\cup \{0\} Homework EquationsThe Attempt at a Solution [/B] So we want to find \lim_{n\to\infty} s_{n} =...

(I) Find the limit (x,y)->(0,0) of F, then prove it by definition. (II) Find the limit and prove it by definition of: as (x,y) approach (C,0), C different from zero. I have previously asked it on Quora, but it doesn't appear to have answers any...

Hello All, I had been reading a book on Machine Design. I understand that at high temperatures, yield strength of the material drops. The behaviour of the fatigue strength i.e. the drop in fatigue strength may at times be taken to be of same proportion as that of yield strength. It is also...

I tried to find the integral of x^m using the definition of Riemann summation. Everything went smoothly until the limit of ∑n=1kn^m divided by k^( m+1), when k approached infinity, showed up. It is clear that it approaches to 1/m+1, but it has to be proved, of course. One could induce that fact...

Homework Statement ##\lim x \to \infty \frac{\sqrt{x+1} - \sqrt{x}}{\sqrt{3x + 5} - \sqrt{3x + 1}}## Homework EquationsThe Attempt at a Solution ##\lim x \to \infty {\sqrt{x+1} - \sqrt{x}} * \lim x \to \infty \frac{1}{\sqrt{3x + 5} - \sqrt{3x + 1}}## ##\lim x \to \infty \frac{(x+1) -...

Homework Statement Verify the following assertions: a) ##x^2 + \sqrt{x} = O(x^2)## 2. Homework Equations If the limit as x approaches ##\infty## of ##\frac {f(x)}{g(x)}## exists (and is finite), then ##f(x) = O(g(x))##. The Attempt at a Solution Let ##\epsilon > 0##. We solve for ##\delta##...

Hello. I have problem with this integral : \lim_{n \to \infty } \int_{\mathbb{R}^+} \left( 1+ \frac{x}{n} \right) \sin ^n \left( x \right) d\mu_1 where ## \mu_1## is Lebesgue measure.

Homework Statement [/b] This is mentioned in my maths book, I m not able to understand it what they did. Homework EquationsThe Attempt at a Solution

Hi, Let the following function: X = ∑^{L}_{k=1} f(k)/L, where f(k) is a continuous random function and L is a random discrete number. Both L and f(k) are non negative random variables. Thus, X is the average of f(k) with respect to L. Is it right to say that X equals (or approximately) to...

I have a presentation with a 2 minute time limit, but I keep going over, and I'm a bit worried because I have to memorize it and I can barely fit it in just reading it aloud. I would really appreciate any tips to make it a bit faster! Thanks! P.S. also how would I read a quote with ellipses in it?

I've always read that these two theories are incompatible, and how General Relativity works for large scales while Quantum Theory represent reality in extra-small cases. So my question is where is the limit where General relativity ceases to exist and Quantum Theory gives a better portrait of...

Please explain the above limit problem.i am able to understand last steps but can't get initial 4 steps.

Hello, I would like to begin by saying that this does not fall into any homework or course work for me. It is just my interest. I need to prove that limit of a constant gives the constant it self. Can some one provide a link? I have exams or I would have searched myself but unfortunately I don't...

What do I have to do if I want the EFE's to approximate a weak gravitational field, where for example, an inversely proportional to the cube ( ##1 / r^3## ) of the distance law between the masses applies?

Hey suppose I have sequence An limAn,n→∞ = ∞ Is it possible to find a sequence which makes: lim (An/An+1) ,n →∞ = ∞? I tried to search a sequence like that and could not find, but I don't know how to prove that this is can not be happening. could you help please?

Hi, I was looking for a symbol in math that is commonly applied when a limit to a function does not exist. Is there such a symbol? I could not find any.

I need to prove that the limit of the sequence is as shown(0): 1.limn→∞ n*q^n=0,|q|<1 2.limn→∞ 2*n/n! but I need to do this using the convergence tests. With the second sequence I tried the "ratio test", and I got the result limn→∞ 2/n+1 which means that L in the ratio test is 0 and so it...

In pair production, if the photon has an energy greater than 1.02 MeV, why can't a lower energy photon remain after creation of the electron-positron pair? For example, if you have a 10 MeV photon interacting with a carbon nucleus, why are the stated products of pair production the carbon...

hey I am trying to calculate the limit of : limn→∞(1/2+3/4+5/8+...+2n−1/2^n) but I am not sure how to solve it, I thought to calculate 2S and than subtract S, but it did not worked well. I did noticed that the denominator is a geometric serie,but I don't know how to continue. could you help?

Hello . I have problems with two exercises . 1.\lim_{t \to 0 } \frac{2v_1-t^2v_2^2}{|t| \sqrt{v_1^2+v_2^2} } Here, I have to write when this limit will be exist. 2.\lim_{(h,k) \to (0,0) } \frac{2hk}{(|h|^a+|k|^a) \cdot \sqrt{h^2+k^2} } Here, I have to write for which a \in \mathbb{R}_+ this...

Homework Statement As the title says, I'm trying to calculate the fundamental noise limit for an ideal photodetector, by specifically looking at the rate of incidence of annihilation of photons (and subsequent excitation of conducting electrons) on the detection surface. Since I'm looking for...

Note: this is QM question, not about stellar science. I am not asking what are the lightest neutron stars found in the Universe. The same star (say, 1 sun mass) can exist both in a form of a white dwarf and a neutron star. Both states are stable. However, let's say I start to stripe outermost...

Remember to use the appropriate packages; these are in similar post if a mod wants to add the link if you choose to use Latex. Here is the PDF \begin{document} \begin{center} {\LARGE Epsilon-Delta Proofs \\[0.25em] Practice} \\[1em] {\large Just for practice, don't use Google to cheat!}...

Consider the summation ∑,i=0,n (t^(n-i))*e^(-st) evaluated from zero to infinity. You could break down the sum into: (t^(n))*e + (t^(n-1))*e + (t^(n-1))*e + ... + (t^(n-n))*e ; where e = e^(-st) To evaluate this, notice that all terms will go to zero when evaluated at infinity However, when...

I don't understand the difference between the elastic limit and the yield point. I understand that if you stretch a material within the elastic limit, then the material should return to its normal shape. However, the yield point is described as the point at which a permanent increase in length...

Let $S_n(k)$ be defined by: $S_n(k) = 1 + 2k+3k^2+...+(n+1)k^n$, where $|k| < 1$ and $n \in \Bbb{N}$. Derive a closed form for $S_n(k)$ and find the limit: $$\lim_{{n}\to{\infty}}S_n(k)$$.

Hi all, I work as a cardiac sonographer. I've been struggling to understand a concept as dictated in ultrasound textbooks and it regards the Nyquist limit. During my work I observed that when I increased my ultrasound transducer frequency (e.g. from 1.7 MHz to 3.0 MHz) when using pulsed wave...

Homework Statement First part (a>1) of the proof: Denote h = a^(1/n) - 1> -1 Then a = (1+h)^(n) >= 1+nh so h <= (a-1) / n Assume a > 1, so that 0 <h <= (a-1)/h n tends to infinity By sandwich principle, lim n tends to infinity of h is 0 Homework EquationsThe Attempt at a Solution Why is h >...

Homework Statement Prove ##\lim_{n\rightarrow +\infty}\frac{\mathbb{E}(L_n)-L^*}{\sqrt{\mathbb{E}( ( \eta_n(X)-\eta(X) )^2 )}}=0## if ##\eta_n## verifies ##\lim_{n\rightarrow\infty} \mathbb{E}( ( \eta_n(X)-\eta(X) )^2 )=0## Homework EquationsThe Attempt at a Solution The idea might be to use...

Hello! I am reading A first course in General Relativity by Schutz and at a point he proves that for a weak gravitational field and assuming ##\Lambda = 0## we have ##\Box \bar{h}^{\mu \nu} = -16\pi T^{\mu \nu}##. Leaving the notations aside, he says that for a weak gravitational field (and...