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 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...
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}\\...
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...
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
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...
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
evaluate lim2x^2 as x approaches 3 using formal definition (epsilon and delta) of limit
Homework Equations
The Attempt at a Solution
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...
Homework Statement
Prove the following states directly using the formal e, d definition
\lim_{x\rightarrow 8} \sqrt{x + 1} = 3
Homework Equations
The Attempt at a Solution
If 0 < |x-8| < d
Then 0 < sqrt((x+1) - 3) < e
Let e be given
3 < sqrt(x+1) < e + 3
9 < x + 1 <...
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}...
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...
[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...
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...
Hi,
Why is it, that when ever epsilon-delta proofs are done, once delta is found in terms of epsilon, it is reinputed through again? Is there any point to this really?
I am trying to show that a certain function, f(x) has a limit that approaches 1. Does anyone have any sites i can look at for epsilon delta proof for 3-space? I've saw the ones for two space, but they aren't really helping me out in this pickle..
thanks.
I must prove \lim_{x\rightarrow 3\\} x^2 = 9
I get this...
\mid x+3\mid\mid x-3\mid < \epsilon if 0< \mid x-3 \mid < \delta
then it says with the triangle inequality we see that
\mid x+3\mid = \mid (x-3)+6\mid \le \mid x-3\mid +6
therefore if 0< \mid x-3 \mid < \delta , then...