Epsilon Definition and 222 Threads

Homework Statement Prove, using the formal definition of limits: If http://rogercortesi.com/eqn/tempimagedir/eqn4201.png and c>0, then [PLAIN]http://rogercortesi.com/eqn/tempimagedir/eqn4201.png (add the constant beside f(x) here, I couldn't get the equation generator to cooperate)...

Homework Statement Prove, using the formal definition of limits: If lim (x->inf) g(x) = inf and g(x) leq f(x) for x->a, then lim (x->a) f(x)=inf. leq = less than or equal to. Homework Equations The Attempt at a Solution Honestly, I'm not even sure where to start on this one. Anyone bored...

I'm sick of still not getting this. I bombed the epsilon delta part of my mid term. A site where it gives many problems on epsilon delta and solutions would be amazing.

The problem is: lim as x→- ∞ (-5x/x-2)=-5 And I have to find the best interval of solutions for N Relevant equations: if x>N then |(-5x/x-2)-(-5)|<ε My attempt: |(-5x/x-2) - (-5)|<ε |-10/x-2|<ε x-2< 10/ε as x→-∞ we can assume that x-2<0 x-2<10/ε x< (10/ε)+2...

Need help proving lim(x)->(a) sqrt(x)=sqrt(a) using epsilon delta definition. Homework Statement Prove that the limit of \sqrt{x} is \sqrt{a} as x approaches a if a>0 Homework Equations in words By the epsilon delta definition we know that the distance between f(x) and the limit...

Homework Statement This is my first delt/epsilon proof ever, so please understand if I seem ignorant. e=epsilon d = delta Let f(x) = 1/x for x>0 If e is any positive quantity, find a positive number d, which is such that: if 0 < |x-2| < d, then |f(x) - 1/2| < e Homework...

"Except on a set of measure epsilon" vs "Almost Everywhere" There are certain results in analysis which say that a property P holds everywhere except on a set of arbitrarily small measure. In other words, for any epsilon you can find a set F of measure less than epsilon such that P holds...

first of all i don't know anything about this epsilon and delta method.explain this a bit. secondly i have been given a problem involving this method: f(x)=x^2 given: limit x-->2 [x^2] = 4 a) what is the value of x' such that f(x')= 4 + .01? find \delta=x'-2 b) what is the value of...

Homework Statement Suppose |f(x)-5|<0.1 when 0<x<5. Find all values \delta>0 such that |f(x)-5|<0.1 whenever 0<|x-2|<\delta Homework Equations The Attempt at a Solution I know that 0<|x-2|<\delta 2-\delta<x<2+\delta \delta=2 but how does this part of the equation help me find...

Hello, I have stumbled upon a couple of proofs, but I can not seem to get an intuitive grasp on the what's and the whys in the steps of the proofs. Strictly logical I think I get it. Enough talk however. Number 1. "Let f be a continuous function on the real numbers. Then the set {x in R ...

Hey So for those that don't know, I'm reading this from Atomic Physics, basically where they teach you how the size of a nucleus was determined by shooting alpha particles at it. due to repulsion an alpha particle can get only 'so-close' to nucleus(they're both positively charged), and the the...

What does that mean when there's an \epsilon in the complexity, such as O(n^{2+\epsilon}) for every \epsilon >0

Homework Statement Prove the function f(x)= { 4 if x=0; x^2 otherwise is discontinuous at 0 using epsilon delta. Homework Equations definiton of discontinuity in this case: there exists an e>0 such that for all d>0 if |x-0|<d, |x^2-4|>e The Attempt at a Solution I'm confused...

By supposing there is a solution to Fermat's Last Theorem then according to Frye you can create an elliptic curve that isn't modular. Taniyama-Shimura says that all elliptic curves are modular, so in proving that that Frye curve is not modular which was done by Ribet don't you disprove the...

Homework Statement Hi! I am new to Real Analysis. Please let me know if my solution is alright. Thanks. epsilon=e Show that |x-a|< e IFF a-e < x < a+e The Attempt at a Solution Assume |x-a|< e. Prove, a-e < x < a+e |x-a|< e -e < x-a < e a-e < x < a+e Assume a-e < x < a+e...

Homework Statement #8 (4x+1)/(3x-4)=4.5 Homework Equations The Attempt at a Solution 4<(4x+1)/(3x-4)<5 What do I have to do next?

Hi, I have a question about the formulation of the derivative. The definition is f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}[/itex] Lets say this limit exists. Can I write the limit in the typical \epsilon-\delta method as such Given the limit exists, then for all...

Homework Statement find an open interval about x0 on which the inequality lf(x)-Ll<\epsilon holds. Then give a value for \delta>0 such that for all x satisfying 0<lx-xol<\delta the inequality lf(x)-Ll<\epsilon holds f(x)=x2 L=3 x0=-2 \epsilon=0.5 Homework Equations The Attempt...

In Schwinger's classic http://dx.doi.org/10.1103/PhysRev.82.664" on pair production, he inserted an infinitesimal to get the desired pair production rate. (On page 13, he said: "We shall now simply remark that, to extend our results to pair-production fields, it is merely necessary to add an...

Recently in adv calc we have been dealing with the epsilon delta definition for continuity, and my professor said that it is ok to assume that delta<1. I actually used this to show that x^4 satisfies the epsilon delta condition but I'm not quite sure why we can take delta<1. I am sure you guys...

Homework Statement Find sup{\epsilon| N\epsilon(X0 \subset S} for X0 = (1,2,-1,3); S = open 4-ball of radius 7 about (0,3,-2,2).Homework Equations If X1 is in Sr(X0) and |X - X1| < \epsilon = r - |X - X0| then X is in Sr(X0) The Attempt at a Solution This is my first foray into...

Why is it true that: if a+e<b for all e>0 then a≤b? What is the meaning of epsilon here? Thanks!

Hi! Quick question: Does it make a difference if i choose my dim reg. to be D=4-2epsilon or D=4+2epsilon (i suppose in both cases epsilon >0). I mean opinion i should not matter but standard qft books normally don't touch this question very deeply... Cheers, earth2

I have a problem on a take-home test, so I can't ask about the specific problem. So this is just going to be a general, how do I put stuff together problem. I have a function of x and y that maps R2 into R1. The limit as (x,y)->(0,0) is zero, and I've worked through the various paths already...

Homework Statement Show that Re(z) -> Re(z0) as z -> z0 The Attempt at a Solution let epsilon > 0, choose delta = epsilon, so |Re(z) - Re(z0)| = |(z + z')/2 - (z0 + z0')/2| (where z' and z0' are the complex conjugates) |(z + z')/2 - (z0 + z0')/2| = |(z - z0 + z' - z0')/2| < |z -...

Homework Statement Define: f(z) \rightarrow w1 as z \rightarrow z0 and g(z) \rightarrow w2 as z \rightarrow z0 prove that f(z)/g(z) \rightarrow w1/w2 as z\rightarrow z0 The Attempt at a Solution let \epsilon > 0 choose \delta > 0 such that: |f(z) - w1| < ______...

Homework Statement Is my understanding correct? As delta(y) and delta(x) approach X from points to the left and points to the right of X (x is what we wish to find the derivative of) then the x and y values of points to the left and right approach the x and y values of X. And as the...

Homework Statement prove that the lim as x goes to 4 of x^2 + x -11 = 9 This is the example used on Paul's Online Notes on limits in calculus which can be found here http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx (I really like this resource.) Homework Equations Paul...

does the epsilon delta definition of the limit connect to the uncertainty in measurements like this? like if we measure a quantity time with value a with error of + or - delta then my formula will give me v with value L +or - epsilon or is it unrelated?

I won't state the theorem in full but showing that a function is integrable if and only if for any epsilon there exists a partition P such that U(f,P) - L(f,P) < epsilon. I'm finding the proof in the forward direction a bit confusing. If you assume the function is integrable that means that...

So i am almost 3/4 through elementary analysis but i seem to be unable to comprehend the basic definition of convergence of series this is how the defn goes. A sequence (sn) is said to converge to a real number s provided that for each ε > 0 there exists a number N such that n>N implies |sn...

i need to prove that for every delta i call d=delta e=epsilon 1/|x+1|>e we can choosr any e we want so they took e=1/4 but because the innqualitty needs to work for every delta they took x=min{2,(1+d)/2} for d>2 it takes x= 1+d /2 for d<2 takes x=2 uppon what logic they found this...

Homework Statement Design a simple experiment using a variable parallel plate capacitor to measure the value of epsilon naught Homework Equations C=(ε0*A)/d Where C is capacitance, A is the area of the plates, and d is the distance between the plates. The Attempt at a Solution...

This isn't a HW question just something I am curious about. I was looking on wikipedia and found a way to prive the Levi-Citiva Kronecker Delta relation that I hadn't seen before. The site claims \epsilon_{ijk}\epsilon_{lmn} = \det \begin{bmatrix} \delta_{il} \delta_{im} \delta_{in}\\...

Suppose limx->a f(x) = L does NOT equal 0. Prove that there exists a (delta) d > 0 such that 0<|x-a|<d which implies f(x) does NOT equal 0. Does Anybody Know the Proof For This?

Hi, I have a question about the epsilon / delta definition of limits, for example the limit of x as it approaches c for f(c) = L. As I understand it, epsilon is basically the number of units on either side of L on the y-axis that makes a range between L + epsilon and L – epsilon with L being...

Homework Statement Using the definition of |x-a|<delta implies |f(x) - L|<epsilon, prove that lim x->0 x^n*sin(1/x) holds for all n belonging to natural numbers. Homework Equations Definition of a limitThe Attempt at a Solution Ok, so when I see "prove for all n belonging to natural numbers" I...

Homework Statement I am currently having problems with a similar question, and used that post, but I'm finding it hard to solve for x. the question states. if f(x) = 1/x for every x > 0, there is a positive quantity e (epsilon), find the d(delta) quatity such that if 0 < l x - 3 l < d...

Homework Statement Use \epsilon K proof to show: lim \left(\frac{n^2 + 2n + 1}{2n^2 + 3n + 2}\right) = \frac{1}{2} Homework Equations Hint first show \left| \frac{n^2 + 2n + 1}{2n^2 + 3n + 2}-\frac{1}{2}\right| \leq \frac{1}{2n}, \hspace{0.5cm} n\epsilon N The Attempt at a...

I am a first year freshman at UC Berkeley, in Math 1A. We learned the delta-epsilon proof for proving the limit of functions. I won't go through a whole proof or anything, but the general idea is you have a delta that is less than |x-a| (and greater than zero) and an epsilon less than |f(x)-L|...

Homework Statement Proove the limit as x approaches 4 for f(x)=x^2-8x= -16 Homework Equations Definition of Precise Limits The Attempt at a Solution I know that I want x^2-8x+16 (after moving the -16 over per the limit definition) to look like |x-4| Factoring gets me (x-4)(x-4)<e Because...

Homework Statement Prove that lim x->3 of (x^{2}+x-5=7Homework Equations 0<x-c<\delta and |f(x)-L|<\epsilonThe Attempt at a Solution The preliminary analysis. The first equation in the relevant equations becomes 0<x-3<\delta And the second equation becomes |(x^{2}+x-5)-7|<\epsilon...

Hello all, My question is as follows: f:[1,\infty) is defined by f(x)=\sqrt{x}+2x (1\leqx<\infty) Given \epsilon>0 find \delta>0 such that if |x-y|<\delta then |f(x)-f(y)|<\epsilon It seems I am being asked to show continuity, and not uniform continuity, so my approach is this, but I am...

Homework Statement For: \lim_{x \to 1^{-}} \frac {1}{1-x^{2}} = \infty Find \; \delta > 0 \; such that whenever: 1-\delta<x<1 \;\; then \; \frac {1}{1-x^{2}} > 100 Homework Equations |x-a| < \delta |f(x)-L| < \epsilon The Attempt at a Solution So as it is set...

Homework Statement Ok so this may get a little drawn out here because my book only gives me one example and I guess I can't decipher its meaning. So here is the example they give: For \;\; \lim_{x \to 2} x^{2} = 4 Find a \;\; \delta > 0 \;\; such that whenever 0 < |x-2|< \delta, \;\;\...

The question is: Suppose f(x) <= g(x). Prove that lim [x->a] f(x) <= lim[x->a] g(x). I've been able to prove it by contradiction. I let lim [x->a] f(x) = L and lim[x->a] g(x) = M and I suppose that L > M. I then went on to choose epsilon = (L - M)/2 and a contradiction easily follows. But...

Homework Statement \mbox{Prove that}\,g^{ij} \epsilon_{ipt}\epsilon_{jrs}\,=\, g_{pr}g_{ts}\,-\,g_{ps}g_{tr} Notation : e_{ijk}\,=\,e^{ijk}\,=\,\left\{\begin{array}{cc}1,&\mbox{ if ijk is even permutation of integers 123...n }\\-1, & \mbox{if ijk is odd permutation of...

I'm learning how to find delta from a particular epsilon. I'm not understanding a step in the solution for the problem listed below: Here's the problem: lim(x→3)x^2=9 Solution: |x^2-9|<.05 -.05<x^2-9<.05 2.9916..<x<3.0083 2.9916..-3<x-3<3.0083..-3 -.0083..<x-3<.0083.. delta=.0083...

I seem to have a silly problem.In Gaussian units, there's no epsilon or mu factor in the equations, so esu must be medium dependant.Now if this is true, then I can "produce" or make "vanish" charges just by switching between media which obviously isn't true.So the mistake?

so 0 < l x-a l < delta and l f(x)-L l < epsilon What I don't understand is how come deltas and epsilons can't be greater than or equal to their respective differences?