What is Limits: Definition and 1000 Discussions

My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it. n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?

Homework Statement http://img831.imageshack.us/img831/8131/onesided.png Homework Equations The Attempt at a Solution I am quite stumped on this problem. I don't think you can bring the limit inside the f(g(x)) function unless f(x) is continuous at the point about which the limit...

\lim_{n\rightarrow 0} {\frac{√(x+4) - 2}{x}} The answer is supposed to be 1/4. When I work it this way: (√(x+4) - 2]/x )(√(x+4) + 2]/√(x+4) +2] and then put in 0 I get 0..

Homework Statement R is the region bounded by y=x^2 and y=4. evaluate the double integral of f(x,y)=6x^2+2y over R After drawing the region I was wondering if I could just work with the first quadrant and then double my solution, because both y=x^2 and y=4 are even functions so my question is...

Homework Statement f is differentiable in ##\mathbb{R^+}## and ##\displaystyle \lim_{x \to \infty} (f(x)+f'(x))=0## Prove that ##\displaystyle \lim_{x \to \infty}f(x)=0## The Attempt at a Solution I can split the limit in two: ##(\displaystyle \lim_{x \to \infty}...

In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a) to d/dt∫(b to a) P(x.t) dx =...

Homework Statement Find the limit of ##1): \displaystyle \lim_{n \to +\infty}(\frac{f(a+\frac{1}{n})}{f(a)})^{\frac{1}{n}}## ##2) \displaystyle \lim_{x \to a} (\frac{f(x)}{f(a)})^{\frac{1}{ln(x)-ln(a)}}(=1^{\infty})## I am not quite sure if i can solve it the way I did, it has been to easy...

Hi all, I'm trying to integrate the function below with respect to x exp(ix)-exp(-ix) With infinity and negative infinity as the limits. Would the integration be possible?

Homework Statement I did two attempts. I find attempt no. 1 slightly fishy and attempt 2 more rigorous. Can anyone tell me what's wrong with attempt no. 1? The Attempt at a Solution Attempt no. 1: Attempt no. 2:

Homework Statement find the limits on spherical coordinates. where ε is the region between z²=y²+x² and z = 2(x²+y²) no matter what i try i can't seem to find the limits, especially for "ρ", so far i got 0<θ<2Pi and 0<φ<Pi.

Homework Statement The problem is to solve the integral. First I did coordinate transformation by finding jacobian = (1/4)(x2 + y2). The problem is, I do not know the limits of integration after transformation...I tried using a graphical approach: by considering 2 cases: y>x and y<x and...

So I am trying to understand how and why the limits of surface and volume integrals come about. I think I came up with a easy to understand argument but not a mathematically sound one. Frankly its a little dodgy. Can anyone provide feedback on this argument or provide a better and possibly more...

I've come up with an idea for a sci-fi story that I'll probably never finish because I'm lazy, but I love the idea. "In a dying universe, there existed a race of intelligent beings. They absorbed all scientific knowledge, but were unable to prevent their demise. In order to continue their...

In this link: http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw3sum06.pdf For number 8.4... Why don't we just say... |s_n||t_n| < \frac{\epsilon}{M} M = \epsilon? Thanks in advance

Homework Statement Normed space (l^\infty,\|\cdot\|_\infty) with subspace S\subset l^\infty consisting of convergent sequences x=(x_n)_{n\in\mathbb{N}}. Given a sequence of maps A_n:l^\infty\to\mathbb{R} defined as $$A_n(x)=\sup_{i\in\mathbb{N}}\frac{1}{n}\sum_{j=0}^{n-1}x_{i+j}$$need to...

Homework Statement Let A, B be subsets of ℝ and f : A → ℝ and g : B → ℝ and f(x)\inB for every x \in A. Prove: If f(x)→L as x → a, for x\in I and g is continuous at L \in B then lim x->a g(f(x)) = g(lim x->a f(x)). Homework Equations f is said to be continuous at a point a iff given ε>0 there...

Homework Statement I have the double integral, ∫∫sqrt(x^2+y^2) dxdy, and the area D:((x,y);(x^2+y^2)≤ x) Homework Equations The Attempt at a Solution By completing the squares in D we get that D is a circle with origo at (1/2,0), and radius 1/2. Then I tried changing...

I have the double integral, ∫∫sqrt(x^2+y^2) dxdy, and the area D:((x,y);(x^2+y^2)≤ x) By completing the squares in D we get that D is a circle with origo at (1/2,0), and radius 1/2. Then I tried changing the variables to x=r cosθ+1/2, y=r sinθ and J(r,θ)=r which leads to a not so nice...

My limits of integration for my angle I chose to be from pi to 0 then I got the negative answer from what was in the book.. Shouldn't that be correct because we are integrating from -3 to 3?

Homework Statement \int_0^2 \int_0^\sqrt{2x-x^2} xy,dy,dx I know the answer, but how does the 2 in the outer integral become pi/2?? I'm fine with everything else, I just can't get this...

Homework Statement I'm having trouble with these here.. it's been a while since I've done sequences and I can't seem to make this work with Standard Limits equations. Clearly the answer given by Wolfram solver is there after the = but i'd like to know the reasoning behind it. Anyone that...

Hi, I am plotting 3 graphs in MATLAB using plotyy as [ax h1 h2] = plotyy(x1,Ftemp,x2,Fsnow); hold(ax(2), 'on'); h3 = plot(ax(2),x1,Fprec); I am thus adding the third graph to the right hand y-axis. I then set the limits and tickmarks for the right hand y-axis as set(ax(2), 'xlim'...

Homework Statement (Between 0-3) ∫x3/√(x2+9)The Attempt at a Solution I attempted U sub, but that didn't work. Neither did integration by parts; however, I do remember my teacher using a method involving sub'ing an "x" or something. Anybody? Will edit in attempts as I search YouTube for...

How we get relation \lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)? Where ##\mathcal{L}\{f\}=F##.

I am modelling the atmosphere as a perfect, static gas subject to uniform gravity, assuming ideal gas equation, the density is found to follow: p=A*exp(-z/H) where A is a const, z is the heigh, and L is the scale height. I want to know when this approximation breaks down! at what density? i am...

Is it possible for a telescope to resolve images beyond the diffraction limit? In other words, is the information in the light entering a telescope insufficient to resolve beyond the diffraction limit, or is information lost when the light is focused onto a screen? Attached to this post is a...

okay, so I'm at the most elementary stage of learning limits and there are things which leave me baffled at times, namely two. 1. lim (x -> a) f(x) = lim (x+k -> a+k) f(x) how? the physical reason behind this? 2. the theorem to evaluate limits of the form --- 1^infinity if f(x)=g(x)=0...

Homework Statement If lim f(x) as x->5 = -1/2 and lim g(x) as x->5 = 4 find lim [f(x)-g(x)] as x->5 Homework Equations The Attempt at a Solution My question: Am I supposed to substitute f(x) by -1/2 and g(x) by 4 and have [-1/2 - 4]?

Hi, Trying to find all partial limits of cos(pi*n/3), I separated it into: a_3k -> -1 a_6k -> 1 Is this a valid approach? Are there any other partial limits?

Homework Statement Evaluate: \lim_{(x,y)\to(0,0)} \sqrt{x^2+y^2}\sin \frac{1}{\tan xy} **Apologies that this Tex didn't come out, I can't see where the typos are**Hopefully you can still determine the function I am trying to write** The Attempt at a Solution So, I can see...

Homework Statement I found that the domain of f was defined for all reals x<-1/3 and x>1/3. Now, I need to find the limits and vertical asymptotes of ##\lim _{\chi \rightarrow \dfrac {1} {3}}\dfrac {x+2} {\sqrt {9x^{2}-1}}## According to Wolfram Alpha, there is no limit. But, I found that the...

I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and 10 of the attached excerpt from Dummitt and Foote. Does anyone have a simpler or more intuitive definition of these two notions, or just an explanation of Dummit and Foote's...

Homework Statement Find the limits of this region of integration, and write all possible equivalent iterated integrals given combinations of dz, dy, and dx. Homework Equations none that are really 'equations'? The Attempt at a Solution In particular, I'm having trouble with the...

Homework Statement http://store2.up-00.com/Sep12/JB498124.jpg 2. The attempt at a solution No attempts because i can't understand how to solve it

Hi, I was wondering about one particular example of this interchange. In Mallat's book, at the proof of Poisson Formula it's visible that the equation at the beginning of the 42nd page features the limit outside of the integral. It is my understanding that this limit had to be in...

Homework Statement Determine the lowest derivative order for which the limit towards 0+ of the nth order derivative of f is nonzero (or otherwise does not exist). f = e^{\frac{-1}{x^{2}}} Homework Equations lim_{x\rightarrow0+}\frac{d^{n}}{dx^{n}}e^{\frac{-1}{x^{2}}} The Attempt at...

Hello, Say f(x) is defined only for x in [a, ∞]. lim x->a+ f(x) = c and lim x->a- f(x) obviously doesn't exist. Do we say that lim x->a f(x) exists or not? Thanks.

$\lim\limits_{n\to\infty}\frac{3n+5}{2n+7}=\frac{3}{2}$ How does one use a delta epsilon proof for a limit at infinity?

Homework Statement \lim_{x \to \infty} \frac{2x}{\sqrt{x+2} + \sqrt{x}}\\\\\\ Homework Equations The Attempt at a Solution \lim_{x \to \infty} \frac{2x}{\sqrt{x+2} + \sqrt{x}}\\\\\\ \lim_{x \to \infty} \frac{\frac{2x}{x}}{\sqrt{\frac{x}{x}+\frac{2}{x}} + \sqrt{\frac{x}{x}}}\\\\\\...

1. Does the series from n=1 to ∞ of (1/2+(-1)n)/n converge? 2. Am I able to split up the series into Ʃ1/2n + Ʃ(-1)n/n even though they are not convergent? I'm not sure how else to prove for convergence. I have tried all the tests...

Homework Statement http://puu.sh/1irk2 Homework Equations The Attempt at a Solution I am having trouble doing this question. I tried doing the L'Hopital but didn't work. When I subbed in 0 in the function, I got 0/0. first time: I got that: http://puu.sh/1iroz It still...

Homework Statement Prove that if f: R->R is an even function, then lim x->0 f(x)=L if and only if lim x->0+ f(x)=L. Homework Equations The Attempt at a Solution So far I have: If f is an even function f(x)=f(-x) for x in domain of f. Then I am trying to apply the limit...

cn= (4n)/(n+4n^(1/n)) When i set it up i think i should use l'hopital but I am confused what to do with the 4n^(1/n) term. an=(7^(2n))/(n!) I know this is a geometric sequence and top and bottom increase initially then tend to 0, but I am lost on how to show the work. should i expand...

Homework Statement use the formal definition to show that lim as t goes to infinity of (1-2t-3t^2)/(3+4t+5t^2) = -3/5 Homework Equations given epsilon > 0, we want to find N such that if x>N then absolute value of ((1-2t-3t^2)/(3+4t+5t^2) + 3/5) < epsilon The Attempt at a Solution...

Homework Statement Let f be a continuous function on ℝ. Suppose that \mathop {\lim }\limits_{x \to - \infty } f(x) = 0 and \mathop {\lim }\limits_{x \to \infty } f(x) = 0. Prove that there exists a number M > 0 such that \left| {f(x)} \right| \le M for all x \in ℝ. Homework Equations...

Homework Statement This isn't really homework, but a question I came upon when doing my homework. How can I go from an integral with limits 0 and a: \int_0^a f(x) dx to something with limits 0 and \infty (still giving the same answer) c\int_0^\infty f(u) du , where c is...

∞ ∫xe^[-x^2] dx -∞ So basically I've solved for everything in this problem and it looks like it should be an indeterminate form and thus divergent. My book and Wolfram both say it's 0 and convergent though. I get it down into: lim [[e^(-t^2)] - e^0]/2 + lim [e^0 - [e^(-v^2)]]/2...

Homework Statement I don't know how to prove that the lim _{x-->a} f(x) =f(a) Homework Equations basically how do we know that the limit of the function near a point a, is f(a). My textbook (Calculus Michael Spivak, 4th ed.) says that we prove this using theorem 2, which is the properties of...

Homework Statement For some reason I'm not grasping the concept of limits when another function is included. For example, lim (x2-y2)/(x2+y2) (x,y)---->(0,0) So pretty much what I did was took the Limit as (x,y=x)------>0 and got 0. Then I took the limit as...

Homework Statement We have the limit of x -> -1 OF (2x+2/x=1) We plug in -1 into the equation and find that it is = to (0/0) therefore it is undefined. We then go into attemting to simplify (2x+2/x=1) and we simplify it to (2/1) so now we know that the limit is undefined at -1 but = 2...