Limits Definition and 1000 Threads

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...

I can't prove it and I've got it by some intuition because not many properties of superlogarithms are known. I don't think anyone can prove it but is there some way to at least check if it is correct. The limit is: $$\lim_{h\rightarrow0}slog_{[log_xx+h]}[log_{f(x)}f(x+h)]$$ where ##slog## is the...

Homework Statement ##\frac{e^x-1}{x}## Evaluate the limit of the expression as x approaches 0. Homework Equations 3. The Attempt at a Solution [/B] The question i have is more theoretical. I was able to solve this problem by expanding the expression into the talyor polynomial at ##x=0##. I...

Hi, I see a formula of gamma function and i have a question. (1) $$\Gamma (s) = \int_{0}^{\infty } e^{-x}\, x^{s-1} dx$$ (2) $$ x=a\, n^{p} \rightarrow dx=ap\, n^{p-1}dn$$ (3) $$\frac{\Gamma (s)}{pa^{s}} = \int_{0}^{\infty } e^{-an^{p}}\, n^{ps-1} dn$$ i understand the formula but...

So we just recently did accumulation points in my maths class for chemists. I understood everything that was taught but ever since I was trying to find a reasonable explanation if the sequence an = (-1)n has 2 accumulation points (-1,1) or if it doesn't have any at all. I mean it's clear that...

For example, if we have something of the form ##\lim_{x -> 0} \frac{f(x)}{g(x)} = \frac{0}{0}## or any other of the indeterminate forms involving 0 and infinity, is there always a procedure (such as l'Hopital's rule) by which we can find out the limit, whether it be a limit that converges to a...

Homework Statement For which value of d does the following limit exist? lim x->d ln [ (x2-13x+30) / (x-d) ] Homework Equations None The Attempt at a Solution I understand how to find limits when the limit goes to a real number, and has a variable in the function to solve for, but not when...

Hello I have three limits to calculate, based on a given limits. What I know is: \[\lim_{x\rightarrow 0}\frac{ln(1+x)}{x}=1\] And based on this, I need to find (without L'Hopital rule), the following: \[\lim_{x\rightarrow 0}\frac{ln(1-x)}{x}\] \[\lim_{x\rightarrow 0}\frac{ln(1+x^{2})}{x}\]...

I know that helicopters cannot fly arbitrary high and 5,000 m are considered as the average limit. In a quick search I also found out, that a AS 350 B3+ has been landed on the Everest (8,848 m, 2005) and another AS 350 has (unofficially) reached 12,954 m in 2012 (official record: 12,442 m by a...

This may be a completely terrible question, but does someone have an idea on the detection capabilities for raman spectroscopy of a bulk sample like human tissue (hair, blood, skin, anything)? I thought it might be fun to see if it were possible to use raman to identify exposures to chemicals...

Hello all I am struggling with these two limits: \[\lim_{x\rightarrow 1}\frac{sin(x^{2}-1)}{x-1}\] \[\lim_{x\rightarrow -1}\frac{sin(x^{2}-1)}{x-1}\] I know that \[\lim_{x\rightarrow 0}\frac{sin(x)}{x}=1\] but can't see how it helps me here. I tried multiplying by x+1 both the nominator...

Hey! :o How could we calculate the following limits without the L'Hospital rule? $$\lim_{x\rightarrow 0}\frac{\sin (x)-x+x^3}{x^3} \\ \lim_{x\rightarrow 0}\frac{e^x-\sin (x)-1}{x^2}$$ Is the only way using the Taylor expansion? (Wondering)

Homework Statement I was sick and missed the lecture so having hard time with this problem @_@. http://i.imgur.com/ByK7iVk.png Homework Equations I don't know how to solve it all the textbook don't have particular problem so having a hard time figuring it out. The Attempt at a Solution My...

Homework Statement I'm trying hard to understand as my professor hasn't taught(nor does my textbook) on how this works. It is known that $$\lim_{x \to 0}\frac{f(x)}{x} = -\frac12$$ Solve $$\lim_{x \to 1}\frac{f(x^3-1)}{x-1}.$$ Homework EquationsThe Attempt at a Solution OK.. so I do this...

I am currently practicing questions on Green's Theorem however in some questions I have been given a finite region enclosed between a parabola and a horizontal line. In these questions I am given 2 values of y but none of x. In one question I was given that y = x^2 and y = 9 and was...

If the results of two separate experiments to measure the same quantity are stated in terms of upper and lower limits at the same confidence level, is it valid to say that the overall upper limit (at the same C.L.) is just the sum of the two individual upper limits? Or is something more...

Homework Statement Problem 1: ##f'(1) = -2## Solve: $$\lim_{x\to0} \frac{f(e^{5x} - x^2) - f(1)}{x}$$Homework EquationsThe Attempt at a Solution Okay so these type of problems really get to me. I'm going to assume some level of substitution are needed but I'm really unsure. I'm guessing that I...

Supposing $x = 0$, do I need limits to solve $\frac{lnx }{x^2} + \frac{1}{2x^2}$? Since $lnx$ does not exist at $x = 0$, then the best we can do is $\lim_{{x}\to{0}} lnx$ which is $0$. But then, $x^2$ at zero equals 0, so we have $0/0$ which is indeterminate, so I need to find...

If I look at the lower limits on the proton decay lifetime \tau set by, say, Super-Kamiokande, I'll see different lower limits depending on what the proton could decay into, eg. \tau_{min}(p \rightarrow K^{+} \overline{\nu}) < \tau_{min}(p \rightarrow \mu^{+} \pi^{0}) < \tau_{min}(p \rightarrow...

Homework Statement Solve the following limit. $$\lim_{x\to0} \space \frac {sin(\pi (Cos ^2 (x)))}{\pi (Cos ^2 (x))}$$ The Attempt at a Solution When I plug ##x\to 0 ## into the limit, I get 0/1... Then what can I do? See here I can't even apply L'Hopital's law... Please help! Here I see the...

hi, I try to calculate the integral $$\int_{0}^{1}log(\Gamma (x))dx$$ and the last step To solve the problem is: $$1 -\frac{\gamma }{2} + \lim_{n\rightarrow \infty } \frac{H_{n}}{2} + n + log(\Gamma (n+1)) - (n+1)(log(n+1))$$ and wolfram alpha tells me something about series expansion at...

Homework Statement can you cancel the x and the |x|[/B] lim x→0 ( x(1-(cos(x))/|x| ) 2. Homework Equations The Attempt at a Solution At first i thought the limit would just be undefined as x approaches 0 but the answer to the problem is actually 0, so can you just cancel the x with the...

I'm reposting this piece of logic because my earlier attempts to get it across failed - nobody got what I was saying. This is about binary sequences like ##010110100111001001...##. All we need to know about a particular sequence is its length, ##N## and the number of 1's it contains. The logic...

Homework Statement Find the following limit: Homework EquationsThe Attempt at a Solution My lecturer has said that rational functions which are a ratio of two polynomials are continuous on R^2. He also said that the limits of continuous functions can be computed by direct substitution. The...

Homework Statement Homework Equations The Attempt at a Solution I think this problem is probably a lot simpler than I am making it out to be. However, when I apply sterling's approx., I get a very nasty equation that does not simplify easily. One of the biggest problems I have though is...

Let's consider superstring theory on a 10 dimensional Minkowski background. And assume there is a D3-brane on which the open strings end and closed strings wander around freely in the background. I want to know, in what limit this gives a supergravity theory in which I can study it by using the...

stuck on how to simplify this?

Does 0.999... equals 1? I know that this is a very basic well known concept but recently I stumbled across a video on Youtube in which the creator argues that the two are not equivalent I posted a comment arguing that in the case of Infinite sum of Σn=0 9(1/10)n you can find the sum of the...

Hi, I'm struggling to prove that a limit ceases to exist as x tends to 0 for the following function: f(x)=\begin{cases}\sin(\frac{1}{x}), & \text{if $x \notin \mathbb{Q}$} \\[3pt] 1, & \text{if $x \in \mathbb{Q}$} \\ \end{cases} I've attempted a proof by contradiction, assuming the limit is...

The first day of physics 211 (calculus based) at my school, our teacher started us out with dimensional analysis and it's importance. We started with the plank length which is in meters and while he didn't specify why, we used the plank constant ,gravitational constant, and the speed of light to...

Homework Statement lim as x tends to -∞ (x)^3/5 - (x)^1/5 Homework EquationsThe Attempt at a Solution The first thing I did was convert it into a radical so it becomes fifthroot√x^3 - fifthroot√x. Then I rationalized to get ( x^3-x)/(fifthrt√x^3+fifthroot√x) . I then divided the top by x^3...

All of the planets should have individual orbits, and should be between the mass of Mercury and Mars. What can their orbits be in AU's? Is there a way to find out how close they can be without destabilizing each other? If we assume the star is about the same size as Sol.

I want to the line integral in the following picture: The field is the blue arrows that go left to right, and the path is the orange line that is going from right to left. Just by looking at the picture, it is clear that the result will be negative, but when I set up the integration this is...

For part of a proof of a differential equations equivalence, we needed to use that $$\int_0^t [\int_0^s g(\tau,\phi(\tau))\space d\tau]\space ds = \int_0^t [\int_\tau^t ds]\space g(\tau,\phi(\tau))\space d\tau$$ I understand that the order is being changed to integrate with respect to s first...

1. Problem statement Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t. p(t) = t + (1/t) at x = t 2. Homework Equations (Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was...

Hi! First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was...

Finding a limit entails understanding how a function behaves near a particular value of x. So what do we mean when we say that a limit doesn't exist (in context to the upper statement)? (From what i studied, i noticed that limit exists only for those functions which have a discontinuity in the...

Hi everybody! I'm preparing an exam of "Analysis II" (that's how the subject's called in German), and I have trouble understanding how to find the limit of a multivariable function, especially when it comes to proving the uniform convergence. Here is an example given in the script of my teacher...

pdf link here https://indico.cern.ch/event/432527/contributions/1071444/attachments/1320402/1979943/Miller_ICHEP2016_AllHadronicSUSY_4Aug2016.pdf Given that they found no SUSY gluinos squarks with this years data set of 18-19 fb-1 + 2-4 fb-1 from last year what are the prospects for natural...

Hi, I am confused by the following diagram when I try to understand it in terms of limit as done by Real-analysis: What I currently understand is as follows: Let the finite length of the straight orange line be X>0. The rest of the non-straight orange lines (in this particular case, the...

I have found that multivariable limits are harder to find and/or prove that something exists. Do you have any recommendations, given questions like "find(if exists) the limit...". For example, I have no idea how to even start thinking about the following limit(if it exists or not, and if it...

I understand that 0.9999... = 1 is true because in limit theory "getting arbitrarily close" means that they actually are equal. I'm also aware of the epsilon-delta definition of limits. But I feel like there are some inconsistencies in this concept; I'll explain using two scenarios. Case 1...

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...

The problem $$ \lim_{x \rightarrow \infty} \left( \sqrt{x+1} - \sqrt{x} \right) $$ The attempt ## \left( \sqrt{x+1} - \sqrt{x} \right) = \frac{\left( \sqrt{x+1} - \sqrt{x} \right)\left( \sqrt{x+1} + \sqrt{x} \right) }{\left( \sqrt{x+1} + \sqrt{x} \right) } = \frac{x+1 - x }{\left(...

The problem $$ \lim_{x \rightarrow \infty} \frac{(\ln x)^{300}}{x} $$ The attempt ## \lim_{x \rightarrow \infty} (\ln x)^{300} = \infty## since ## \lim_{x \rightarrow \infty} f(x) = A## and ## \lim_{x \rightarrow \infty} g(x) = \infty ## thus ## \lim_{x \rightarrow \infty}f(g(x)) = A ##. ##...

Is ## "\frac{0}{\infty}"=0 ## ?

The problem \lim_{x\rightarrow \infty} \frac{x^4 + x \ln x}{x + \left( \frac{2}{3} \right)^x} The attempt \lim_{x\rightarrow \infty} \frac{x^4 + x \ln x}{x + \left( \frac{2}{3} \right)^x} = \lim_{x\rightarrow \infty} \frac{x^4(1 + \frac{x \ln x}{x^4}) }{x + \left( \frac{2}{3} \right)^x}...

Homework Statement : the question wants me to prove that the limit of f(x,y) as x approaches 1.3 and y approaches -1 is (3.3, 4.4, 0.3). f(x,y) is defined as (2y2+x, -2x+7, x+y). [/B] The attempt at a solution: This is the solution my lecturer has given. it's not very neat, sorry...

Hello, I am want to prove that: $$ \sum_{1}^{\infty} \frac{1}{n^{2} + 1} < \frac{1}{2} + \frac{1}{4}\pi $$ Cauchy's Convergence Integral If a function decreases as n tends to get large, say f(x), we can obtain decreasing functions of x, such that: $$ f(\nu - 1) \geqslant f(x) \geqslant...