Epsilon Definition and 222 Threads

Could you help me with the problem? Find delta using the definition of limits, given epsilon = 0,25 lim 1 / (2-x) = -1/3 x->5 Answer should be delta = 1 How can I get it? Thanks.

Homework Statement I need to calculate Ax(BxC) -A, B, C are vectors, apart from bac-cab rule, I need to get it by epsilon ijk -Following I will note it by e(ijk). Homework Equations I expect answerer to know kronecker delta equation and vector multiplications. The Attempt at a...

Homework Statement show that the function F:C\rightarrowC z \rightarrow z+|z| is continuous for every z0\in C2. Proof F is continuous at every z0\in C if given an \epsilon > 0 , there exists a \delta > 0 such that \forall z 0 \in C, |z-z 0|< \delta implies |F(z)-F(z0)|< \epsilon. I know...

Homework Statement Im trying to figure out what the difference is between the following two epsilon delta statements and the kinds of functions they satisfy: For all real numbers x and for all delta>0, there exists epsilon>0 such that |x|<delta implies |f(x)|<epsilon vs. there exists...

Homework Statement Prove that as x approaches 0, sin(1/x) has no limit. Homework Equations |x-a|<d and f(x)-L<e The Attempt at a Solution my teacher explained it, but i didnt quite get where the contradiction is at the end. We chose epsilon to be 1/2

Can someone please explain Epsilon delta definition of limit in detail?

Hi there, I'm having trouble understanding how to prove things using the \delta \epsilon definition. I have read a few other threads and sites, but I can't seem to put it together. For example, I came across this problem, if given limx-->af(x) = L, how would I prove (using delta-epsilon and...

Homework Statement For the limit below, find values of δ that correspond to the ε values. Homework Equations epsilon = .5 and epsilon = .05 The Attempt at a Solution These kinds of problems do you have to use a graphing calculator to figure it out? for epsilon = .05 |(9x + x...

Homework Statement evaluate lim2x^2 as x approaches 3 using formal definition (epsilon and delta) of limit Homework Equations The Attempt at a Solution

Im having trouble proving limits of multivariable functions. I understand the principal behind delta-epsilon proofs but I can't get it to work. Once I set up the inequalities I am stuck. The only example in my book seems very convenient though . 3x^2 * abs(y) divided by x^2 + y^2...

i know how to do basic proofs, but some proofs on the actual limit theorems confuse me. my textbook's choices for delta are very obscure and i have no idea how they even came up with them. for the proof of the limit theorem where the limit of a product of 2 functions is equal to the product...

Homework Statement Let K be a compact sebset of a metric space (X, d) and let \epsilon greater than 0. Prove that there exists finitely many points x_1 x_2, ... x_n \in K such that K is a subset of the union of the \epsilon neighborhoods about x_i Homework Equations N/A The Attempt...

hey if lim (x-->0) f(x) = L where 0 < |x| < d1 implies |f(x) - L | < e how do i prove lim (x --> 0) f(ax) = L? i know 0 < |ax| < |a|d1 d2 = |a|d1 but the textbook says d2 = d1/|a| help you guyssssssssssssssssssssssssssssssss

Given: limit of (sin x)/x as x --> 0 and that ε = .01 Problem: Find the greatest c such that δ between zero and c is good. Give an approximation to three decimal places. Equations: 0 < |x - a| < δ 0 < |f(x) - L| < εAttempt: 0 < |x - 0| < δ 0 < | sin(x)/x - 1| < ε 0 < | sin(x)/x - 1| < .01 0...

Given the limit of \frac{x^2+2x}{x^2-3x} as x approaches 0 equals \frac{-2}{3} and that ε = .01, find the greatest c such that every δ between zero and c is good. Give an exact answer. 0 < |x-0| < δ 0 < |\frac{x^2+2x}{|x^2-3x} + \frac{2}{3|}| < ε |\frac{x(x+2)}{|x(x-3)} +...

Homework Statement Let f: \Re \rightarrow \Re and g: \Re \rightarrow \Re be functions such that lim_{x \rightarrow 1} f(x)=\alpha and lim_{x \rightarrow 1} g(x)=\beta for some \alpha, \beta \in \Re with \alpha < \beta . Use the \epsilon-\delta definition of a limit to prove...

Homework Statement given a function defined by f(x,y) {= |xy|^a /(x^2+y^2-xy), if (x,y) cannot be (0,0) and = 0, if (x,y) = (0,0) Find all values of the real number a such that f is continuous everywhere e= epsilon d= delta In order to prove this, I know I need to do an...

Okay so here's the limit lim(as x --> -1) 2x^2=2 I have |2x^2-2| < 1 2|x + 1||x - 1| < 1 |x + 1||x - 1| < 1/2 and 0 < |x + 1 | < delta -1 - delta < x < -1 + delta |x - 1| < -2 + delta |x + 1| < 1/2(-2 + delta) so is delta = 1/2(-2 + delta) correct...

Homework Statement Prove the follow statements directly using the formal \epsilon , \delta definition. \lim_{x\rightarrow 1} \frac{x + 3}{x^2 + x + 4} = \frac{2}{3} Homework Equations The Attempt at a Solution 0 < |x - 1| < \delta \rightarrow 0 < |\frac{x + 3}{x^2...

Homework Statement Suppose A_n is, for all natural numbers n, some finite set of numbers in [0,1] and A_n intersect A_m={ } if m!=n Define f as follows: f(x) = 1/n if x is in A_n and 0 if x is not in A_n for all n. Prove that the limit as x goes to a of f(x) = 0 for all a in [0,1]...

Hi, Want to show: a<=r However I ended up with such an argument: For each eps>0, a<r+eps. Does this statement imply a<=r?

A positive number epsilon (e) and a limit L of a function f at a are given. Find delta such that |f(x)-L|< epsilon if 0 < |x-a| < delta. \lim_{x->5}, 1/x= 1/5, \epsilon=.05. That implies the following |\frac{1}{x}-\frac{1}{5}|< \epsilon \mbox{ if }|x-5|<\delta. Which implies...

I have started studying maths on my own using a University maths book that may not lend itself to self study. So I was hoping someone could help me with the following.abs{sqrt{x}-2} < .05 if 0 < abs{x-4} < delta. I rewrite this as abs{sqrt{x}-2} < .05 if abs{(sqrt{x}+2)(sqrt{x}-2)} < delta...

Here's an example that helps illustrate my question: Prove: A sequence in R can have at most one limit. Proof: Assume a sequence {xn}n\inN has two limits a and b. By definition: -For any \epsilon>0, there exists an N\inN such that n\geqN implies that |xn-a| < \epsilon/2. -A...

Homework Statement 1) Show that \epsilon_{ijk,m}=0 and (\sqrt{g})_{,k}=0 . Where ' ,k ' , stands for covariant derivative and \epsilon is the epsilon permutation symbol. 2) where the {} is for christoffel symbol of the second kind. Homework Equations The Attempt at a...

I have an example bit I can't quite follow it...? Use epsilon -delta definition of continuity to prove f(x) = 3x^2 - x is continuous at x=2 Ep > 0 and delta > 0 in terms of Ep f(x) -f(2) = 3x^2 - x -(3*2^2 -2) f(x) - f(2) = 3x^2 -x - 10 f(x) - f(2) = (3x + 5)(x - 2) So far so...

Like many people on this forum, i am seemingly having a lot of trouble grasping the concepts of Epsilon Delta proofs and the logic behind them. I have read the definition and i realize for e>0 there is a d>0 such that... 0<sqrt((x-1)^2 - (y-b)^2) < d then f(x,y) - L <e (excuse my use of...

I understand most of the logic behind the formal definition of a limit, but I don't understand the the logic behind an epsilon delta proof. The parts I'm having trouble with are these: 1. How does proving that, the distance between the function and the limit is less than epsilon whenever the...

The epsilon delta rule states \epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp} I am constantly using this but get stuck when it is applied. For example \epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}...

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LaTeX fonts for "epsilon" There are two "epsilons", one that looks like the set membership, and the other that looks like a backwards 3. I want the second one, but my latex software only outputs the first one. How do I change that?

I'm studying limits now (for the first time) and though have understood the intuitive concept of limit, I didn't get at all the epsilon-delta concept. What is epsilon and delta? What is x-2? I didn't get anything at all. So please explain me these in detail. Thanking you in advanced...

This system has been getting a lot of press lately, particularly with regard its planet. Double the rubble: Nearby star system has two asteroid belts http://www.sciencenews.org/view/generic/id/38105/title/Double_the_rubble_Nearby_star_system_has_two_asteroid_belts...

I don't know how yor format this, so: x3 + x2 +x +1 The limit of that function = 0 as x approaches -1 What's the greatest value of delta when epsilon = 0.1? This is what I tried to do: |x3 + x2 + x + 1| < 0.1 -0.1 < x3 + x2 + x + 1 < 0.1 -1.1 < x3 + x2 + x < -0.9 In my...

How does one prove: limit xy = ab x-> a y -> b using the precise definition of a limit? My attempt: |xy-ab|<ϵ for: 0<|x-a|<δ/2 0<|y-b|<δ/2 it follows that: δ/2-a <x< δ/2+a δ/2-b <y< δ/2+b then: (δ/2-a)(δ/2-n) < xy < (δ/2+a)(δ/2+b) (δ^2/4-aδ/2-bδ/2 +ab)...

Okay for a simple finite limit: e.g. lim (3x) = 3 x->1 in the end I say: "Therefore for every |x - 3| < delta, there exists an epsilon such that |3x-3| < epsilon" Hence I can make delta really really small and the y bounds of epsilon will constrain the limit. So let's come to...

Suppose $\lim_n \frac{a_n -1}{a_n +1} = 0$. Prove that $\lim_n a_n = 1$. I am trying to do the algebra so that -a_n < ?? < a_n , but I am having trouble. Am I going about this correctly? I have also tried to solve each separate side of the inequality. I get a_n < (e+1)/(1-e), but this is...

This is a famous proof that utilizes a common notion. Theorem. Limits are unique. let n>N_1 such that blah blah blah is less than epsilon over 2, let n>N_2 such that blah blah blah is less than epsilon over 2. For n> max{N_1,N_2}, blah blah blah < blah = epsilon...

1. The problem statement. Give a complete and accurate \delta - \epsilon proof of the thereom: If f is differentiable at a, then f is continuous at a. 2. The attempt at a solution Known: \forall\epsilon>0, \exists\delta>0, \forall x, |x-a|<\delta \implies \left|\frac{f(x) - f(a)}{x-a}...

[SOLVED] Epsilon Delta Proof Does this limit proof make total sense? Given : "Show that \lim_{x \rightarrow 2} x^{2} = 4." My attempt at it :0<|x^{2}-4|<\epsilon which can also be written as 0<|(x-2)(x+2)|<\epsilon. 0<|x-2|<\delta where \delta > 0. It appears that \delta = \frac...

I can't get my head around the epsilon-delta definition of a limit. Unfortunately I don't have a teacher to ask (I'm teaching this to myself as a self interest) so this forum is my last resort -- google hasn't been kind to me. From what I've seen, I don't really understand how the definition...

I’m going to say from the beginning that I need to hand this problem in. I'm not looking for the answer, I think I already have it, just want a critical eye. I need someone to look over this problem and tell me if it's good. Not just if it's right but if it's perfect. I always get the...

Homework Statement Is this the right direction to prove Given that , prove that . Using the delta epsilon definition to prove that means that, for any arbitrary small there exists a where as: If we choose any constant for (x) called C, as long as C does not equal zero, the...

Homework Statement i have a couple of questions to anser and they start 'Give epsilon - delta proofs that the following functions are continuous at the indicated points.' im guessing its not going to be too hard but what is the name of this epsilon - delta proof so i can search for and...

Homework Statement Prove: \lim_{x \to a} \sqrt{x} = \sqrt{a}, if a>0 Homework Equations |f(x)-L| < \epsilon |x-a| < \delta The Attempt at a Solution |\sqrt{x}-\sqrt{a}| < \epsilon, when |x-a| < \delta |x - 2\sqrt{x}\sqrt{a}-a| < \epsilon^2, when |x-a| < \delta From here I...

Could someone please give me a walkthrough of the following question(and answer)?? I really can't understand it... lim x^2 = 9 x->3 if 0<|x-c|<delta then |f(x) - L|< epsilon so... x^2 - 9 = (x+3)(x-3) |x^2 - 9| = |x+3||x-3| Here's the problem.The book states: An...

I'm having trouble solving this question... If the epsilon ring of Uranus is 75 km wide, how long will it occult a star? Any help would be greatly appreciated.

All known natural materials have epsilon and mu > 0. However, there is an intense effort to manufacture so-called metamaterials, where both of these are <0. In such a case, given n = sqrt[epsilon x mu], one would take the negative root and n is still a real number, but n <0 why do we take the...

How do I write that given a set S, every epsilon neighborhood of infinity (in the complex plane) contains at least one point of S?

Is there a value for epsilon in the equation: k=1/4pi-epsilon?