Limits Definition and 1000 Threads

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 2: The Rudiments of Plane Topology ... I need help with some aspects regarding an example in Palka's final remarks in Section 2.2 Limits of Functions ... Palka's final remarks in...

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 2: The Rudiments of Plane Topology ... I need help with some aspects of a worked example in Palka's remarks in Section 2.2 Limits of Functions ... Palka's remarks in Section 2.2 which...

When replying to this thread: https://www.physicsforums.com/threads/the-nasa-zero-gravity-flight.927136/ I became uncertain of my understanding of the physics after the plane starts to descend. What I imagine happens is that your forward velocity would remain constant and you would be...

Homework Statement https://i.imgur.com/Wx0tkw8.jpg (example 3b) Homework Equations limit of multivariable equation Two path test The Attempt at a Solution My instructor told us that we should only use two paths test only if we predict there isn't any limit... but how can we 'sense' there...

1. Find if the limit exist: sin (x^3 + y^3) / (x + y) (x,y)-> (0,0) So I am starting solving this by using polar coordinates form and I get to lim= sin r^3 ( cos^3θ + sin^3θ) / r ( cosθ + sinθ) = lim r^2 ( cos^2Θ + sin^2Θ) My question is ok so far and how...

Dear all, I have a question concerning calculating the following limit: \lim_{x \rightarrow 0} f(x) = \lim_{x \rightarrow 0} \frac{\sin{(x)}}{x} = 1 Obviously, x=0 is not part of the domain of the function. One way to calculate the limit is using l'Hospital. Another way for these kinds of...

Is there a limit to optical space interferometry? I read this article https://www.noao.edu/meetings/interferometry/workshop-files/Carpenter-Space-comp.pdf about future concepts(which i think is really good). I'm wondering, can optical interferometers have a length of more than 1 light...

I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 4: Limits ... I need help in fully understanding an aspect of the proof of Theorem 4.2.9 ...Theorem 4.2.9 ... ... reads as...

I am reading "Real Analysis: Foundations and Functions of One Variable"by Miklos Laczkovich and Vera Sos ... I need help with an aspect of Example 10.7 (2) ... Example 10.7 (2) reads as follows: In the above text, we read the following: "... ... Since whenever $$\lvert x - 2 \lvert \lt...

I am reading Manfred Stoll's Book: "Introduction to Real Analysis" ... and am currently focused on Chapteer 4: Limits and Continuity ... I need some help with an inequality involving absolute values in Example 4.1.2 (a) ... Example 4.1.2 (a) ... reads as follows: In the above text we read ...

I am reading Manfred Stoll's Book: "Introduction to Real Analysis" ... and am currently focused on Chapteer 4: Limits and Continuity ... I need some help with an inequality involving absolute values in Example 4.1.2 (a) ... Example 4.1.2 (a) ... reads as follows:In the above text we read ...

As I understand, under Newtonian Gravity, there are no limits for the length of the gravitational influence of an object, except the speed of causality and the age of that object. So, considering the Sun as an example, which is roughly 4.6 billion years old, its gravitational influence would...

I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 2: Sequences and Series ... I need help in fully understanding Example 3.4.3 (b) ...Example 3.4.3 (b) ... reads as...

I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 2: Sequences and Series ... I need help in fully understanding Example 3.4.3 (b) ... Example 3.4.3 (b) ... reads as follows: In the above text from Bartle and...

In his book: Introduction to Real Analysis, Manfred Stoll does not prove parts (a) and (b) of Theorem 2.2.6 on the limits to certain special sequences ... I am having trouble getting started on the proof of part (a) ... can someone please help me to make a meaningful start to the proof ...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.7 Part (1) ... ... Exercise 2.2.7 Part (1) reads as follows:I have managed a solution to this...

Homework Statement I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.7 Part (1) ... ... Exercise 2.2.7 Part (1) reads as follows: I have managed a...

From what I understand, machine learning is incredibly good at making predictions from data in a very automated/algorithmic way. But for any inference that is going to deal with ideas of causality, it's primarily a subject matter concern, which relies on mostly on judgment calls and intuition...

Find the limit of 1/(n•cosn) as n tends to +∞. I say the following: 1/[(∞)cos (∞)] 1/∞ = 0 The limit is 0.

Homework Statement Discuss how Newton’s Laws can be used to explain the introduction of transportation safety features such as: Speed Limits on curved ramps Homework Equations Newton's 2nd Law: F=ma The Attempt at a Solution I believe that according to Newton's first law objects that are in...

Hello all, I am in a total state of confusion with regard to this. Here is question. The length of a rod is [11.05 (+/-) 0.2]cm. What is the length of two rods? I want to know should the answer be reported like [22.1(+/-) 0.2] or [22.1(+/-) 0.4]. Regards:)

The "wireless power" thread made me think of this, but I have pondered it before when it comes to microphone arrays etc You can easily find documentation on the interference patterns N in-line sources of waves generate. E.g. The annoying thing here is that you have infinitely extending lobes...

I'm trying to integrate a simple function (x*y) using the Romberg method. Question 1: I want to integrate only x and maintain the argument y present in the rest of calculation, like a global variable. In fortran 77 I would use common. Question 2: How to integrate using arguments in the...

The speed of light (in the vacuum) is a function of the permeability and permittivity of the vacuum. In other mediums the phase velocity will be different. It is assumed (by me) that the speed of a gravitational wave does not change depending on the medium i.e. a gravitational wave would not...

Is it possible to find the limit of (1+1/x)^x as x approaches minus infinity using only the fact that it is e if x approaches infinity?

I know localisation microscopy 'beats' the limit on resolution by activating individual sources and rendering a final image, but what are the limits that prevent the resolution of the images of these individual fluorophores? Is it just the number of photons collected? Cheers

Homework Statement Homework EquationsThe Attempt at a Solution let y = lim x->0+ x^cos(1/x) lny = cos(1/x)*lnx = (x*cos(1/x)) * (lnx/x) x*cos(1/x) = 0 (sandwich theorem) lnx/x = 0 (l'hopital) so lny = 0 and y = 1 Is this correct?

This could as well go to the statistics, but I am looking at it from particle physics point of view... Why adding systematic uncertainties worsen the expected upper limits to the signal strength? I am trying to find where the flaw enters in the following logic: 0. The model most analyses use is...

Homework Statement Homework Equations [/B] Definition: A sequence X_1,X_2,\dots of real-valued random variables is said to converge in distribution to a random variable X if \lim_{n\rightarrow \infty}F_{n}(x)=F(x) for all x\in\mathbb{R} at which F is continuous. Here F_n, F are the...

I have recently been doing some work that involves long, messy manipulations with lots of geometric series. A typical such series, which would only be one of a number of such terms in a formula, is: $$ \sum_{t=h+1}^{T-h} \left(1-(1-\theta)^{T-t-h+1}\right) \\ $$ It's not difficult to simplify...

Homework Statement I'm not sure if this is introductory or not but here goes anyway... So we have this experiment to measure the flow rate of viscous fluids by forcing them up a measuring tube using some compressed air in a drum. The idea is to test the limits of poiseuilles law with various...

I want to ask the limits on the molecule side for single molecule fluorescence microscopy. I am writing a proposal but I lack experimental knowledge since no one in my lab have ever used one. At least how much of an absorption coefficient, with at least how much of a radiative rate is necessary...

Given the de Broile wave matter equation, wavelength = plank's constant / momentum,... 1) what's the maximum distance from the electron until its wave like behaviour stops interfering with its surroundings? 2) why the bigger the wavelength, the more the electron is to interact with its...

Homework Statement This has been driving me crazy I can't for the life of me figure out how to convert the limits of this integral into spherical coordinates because there is an absolute value in the limits and I'm absolutely clueless as to what to do with with.Homework Equations $$\int_{\frac...

1. $$\log_{e}\left({x}\right)\to-\infty$$ as $$x\to{0}^{+}$$ 2. $${x}^{x}\to\infty$$ as $$x\to\infty$$ I know how to prove that $$\log_{e}\left({x}\right)$$ approaches $$\infty$$ as x approaches $$\infty$$ by using the definition given in the book, not sure how to use that to prove the...

I'm just starting to learn about the physics behind Faraday's laws and magnetic flux and it's gotten me thinking a lot about superconductors. I know that you can store energy in a superconductor in the form of magnetic fields since a current in a superconducting loop will persist indefinitely...

Homework Statement I have a series of problems 1.problem. When this number is summed with its square. The summ is the least possible. 2.problem Find positive number which substraction with its third power would be the greatest. 3.problem Find to numbers which x+y=5 but multiplication is the...

General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.

The definite integral of a function ##f(x)## from ##a## to ##b## as the limit of a sum is: $$\int_a^bf(x)dx=\lim_{h\rightarrow 0}h(f(a)+f(a+h)+.. ..+f(a+(n-2)h)+f(a+(n-1)h))$$ where ##h=\frac{b-a}{n}##. So, replacing ##h## with ##\frac{b-a}{n}## gives: $$\lim_{n\rightarrow...

Nuclear reactors are licensed with a fixed service life in all countries. This is despite the fact that reactors have widely varying ages (some plants have taken decades to complete), varying use cycles (not all plants run at 90%+ capacity factor, some are even mothballed), and undergo power...

Hey! :o Could you give me a hint how we could calculate the following limits? $\displaystyle{\lim_{x\rightarrow -1^-}\frac{-x}{\sqrt{1-x^2}}}$ $\displaystyle{\lim_{x\rightarrow -1^+}\frac{-x}{\sqrt{1-x^2}}}$ $\displaystyle{\lim_{x\rightarrow 1^-}\frac{-x}{\sqrt{1-x^2}}}$...

Sorry, I mistakenly reported my own post last time. But later I realized that these limits do work. So, I'm posting this again. I'm using these limits to check second-order differentiability: $$\lim_{h\rightarrow 0}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$$ And, $$\lim_{h\rightarrow...

Is there a way to estimate the upper limit and lower limit of time for doing a work? Suppose we are learning a page of facts and want to estimate the upper and lower limit of time taken to do so. If we start estimating the time we will find that the pages are learned in some variable periods of...

Simple premise: take ohms law with a purely resistive ac circuit. 1 volt through in series with a 2 ohm resistor, I have 0.5 amps of current. I want to maintain constant power. In practice, "how low can I go" with the voltage to increase the current? There's probably many variables I'm missing...

I understand the conditions for the existence of the inverse Laplace transforms are $$\lim_{s\to\infty}F(s) = 0$$ and $$ \lim_{s\to\infty}(sF(s))<\infty. $$ I am interested in finding the inverse Laplace transform of a piecewise defined function defined, such as $$F(s) =\begin{cases} 1-s...

This is mostly a procedural question regarding how to evaluate a Bromwich integral in a case that should be simple. I'm looking at determining the inverse Laplace transform of a simple exponential F(s)=exp(-as), a>0. It is known that in this case f(t) = delta(t-a). Using the Bromwich formula...

This thread is to serve as both a compilation and ground of discussion of key experiments, both historical and planned, which attempt to probe possible macroscopic limits of QM, taking into account e.g. some particular gravitational/optical/mechanical/superconducting/etc aspect and/or...

Homework Statement limit (x -> 0 y -> 0) of xy/sin(x+y) Homework Equations None that come to mind but maybe Lopital's Rule The Attempt at a Solution I know that the limit does not exist but I am having trouble figuring out how to show that it does not using the line x=y gives x^2/sin(2x)...

Homework Statement Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path. I have some differential function dZ where Z = Z(x,y) Homework EquationsThe Attempt at a Solution [/B] If I need to integrate, then I need to find the limits of...

I'm trying to understand why the ## \lim_{n \rightarrow \infty} ( \displaystyle \frac {n+1}{n-1} ) ## equals the indeterminate form 1∞? I ask because we have started going over sequences and it was used as an example. I understand how to go from here- taking the ln of both sides and using...