Epsilon Definition and 222 Threads

consider Coulomb's law in medium. You find there epsilon. Consider the expression for the magnetic field generated by an electric current in the same medium (nonconducting, homogeneous and isotropic). Please let me know how do they transform when we consider them from two inertial reference...

Homework Statement Given that lim f(x)=L as x approaches a , prove that lim (x+f(x))=a+L as x approaches ahttps://www.physicsforums.com/attachments/9630. Your proof cannot assume that the limit of a sum of two functions is the sum of their individual limits. You must use the delta-epsilon...

Homework Statement find a number delta Homework Equations f(x) = 1/x | 1/x - 0.5 |<0.2 whenever | x - 2 | < delta The Attempt at a Solution how would you factor out a negative exponent? is this possible? i think i can get x out from under the 1/x with using negative...

Can anyone help with these problems 1). use def. delta epsilon proof to prove lim(z goes to z0) Re(z)=Re(z0) This is what I did |Re(z)-Re(z0)| = |x-x0| < epsilon then |z-z0|=|x-iy-x0-iy0|=|x-x0+i(y-y0)|<=|x-x0|+|y-y0|=epsilon + |y-y0| = delta My question is doesn't this delta have to...

I'm supposed to prove that lim x -> -2, x^2+3x+7 = 5 Here's what I have: |x^2 +3x+7 – 5| < ε |x+2| < δ |x^2+3x+2| -> |(x+2)(x+1)| < ε whenever |x+2| < δ |x+1||x+2| < δ |x+1| |x+1||x+2| < δ|x+1| < ε ε / |x+1| > δ , as x -> -2, |x+1| -> 3, therefore: ε / -1 > δ But...

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?

Can anyone help me on this question,Using \epsilon-\delta definition of a limit to show that \lim \frac {2x^3-y^3}{x^2+y^2} = 0 (x,y)\rightarrow(0,0)

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'm have some trouble distinguising definitions and require some help please: is the epsilon-n def. for convergence? is the epsilon-delta def. for continuity? if this is correct could you slighlt elaborate on what it actually means; I'm quite confused and any help would do!:confused:

I need help solving this the sum of the residual values is equal to 0, epsilon used as symbol to represent the residual value in this formula here epsilon = Yi - b1 - b2*Xi b1 = mean value of Y - b2*mean value of X and b2 = (sum of Xi*Yi - n*mean value of X*mean value of Y)/(squared...

OK I probably have some dumb questions here but it might be partially due to the lack of examples at my disposal and minimal explanation in my text. \lim_{x\to{0}}(x+1)^{3} = 1 \mid f(x) - L \mid < \epsilon \mid(x+1)^{3} - 1\mid < \epsilon now I know that delta is as follows: 0 <...

In Coulomb's law the term epsilon zero appears in the denominator and receives the name of [b] permittivity constant [\b]. As it comes from the word permit (allow) then it would seem reasonable, for me at least, to expect that, as epsilon zero increases, the vacuum would be allowing one charge...

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...

I saw this binary with me friend's 10-inch. The secondary looked so blue I could not believe my eyes! Has anyone hear noticed the deep colour of this lovely double star? Eridanus1

Hi all,, I came to College and Calculus started with epsilon and delta at beginning...For few weeks i was not even able to get a pich of understanding of it...But somehow i got it...But i find using Epsilon and delta ..solving a question makes it awkard...i want to know does solving the...

electric field is written as q/4*pi*r²*e0. i guess that 1/4*pi*r² stands for the decrement of flux density, with area of sphere (then it looks like force = "flux per unit area"). i need clarification about the constant epsilon 0. I'm not asking definitions such as "it's electrical...

I really need help on solving this question: Let d and K be given real numbers. Suppose that lim f(x) > K. x->c Show that there is a number h>0 such that f(x) > K for all x in the punctured open interval of width 2h centred...

Can anyone tell me what role epsilon play in a simple harmonic oscillator, and what the formula is relating epsilon to SHO?

It is known that it was Descartes the one that gave the symbol i the connotation of imaginary; in electrical engineering there is the concept of apparent power(MVA) S = P + i Q where P(MW)=generation or consumed power and Q(MVAR) = reactive power and they both can be measured, so they...

Prove that lim_{x \rightarrow c} \ \ \frac{1}{x}=\frac{1}{c} \ ,c\neq0 Proof We must find \delta such that: 1. 0<|x-c|<\delta \ \Rightarrow \ | \ \frac{1}{x}=\frac{1}{c}|<\epsilon Now, 2. | \ \frac{1}{x}=\frac{1}{c}|=| \ \frac{c-x}{xc}|= \frac{1}{|x|} \cdot...

Tensors, a reason of great schism in physics? Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed...

Ok well i did problems like this before but now I am having trouble with this one for some reason. Let f(x) = \frac{1}{\sqrt{x}}. Give a \delta - \epsilon proof that f(x) has a limit as x \rightarrow 4. So the defn of a limit is \forall \epsilon > 0 \exists \delta > 0 such that whenever 0...