Discontinuity Definition and 99 Threads

Hello! This is the first time I write in the forum. I hope to be fully in-topic. I'm dealing with a rectangular waveguide discontinuity: a perfect-conductor plane orthogonal to the propagation direction, with a circular aperture in the centre of the guide section. The structure is symmetrical...

Hi, I think I need some help understanding exactly what my book means when it says "the electric field undergoes a discontinuity passing a surface charge." In fact, using Gauss' law my book directly calculates by how much the field is discontinous, so definitely I must be missing something...

consider this function f(x)=[x[\frac{1}{x}]] ([x] represent greatest integer less than or equal to x or in short GIF ) internal brackets over 1/x and external brackets are around full body of function. discuss on these points(means either are these correct incorrect) Statement 1: this function...

consider a particle in one dimention. there is a dirac delta potential such as V=-a delat(x) the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively. so the differential of the wave functions are not continious at x=0. what is the justification here?

Homework Statement Suppose f: ℝ → ℝ takes on each of its values exactly twice; that is, for each y in ℝ, the set {x: y = f(x)} has either 0 or 2 elements. Show that f is discontinuous at infinitely many points. Homework Equations I don't know if this is relevant, but in the prior text to...

Homework Statement Prove that f(x) = 1/(x^2) is not continuous at x = 0 using the epsilon and delta definition of a limit Homework Equations definition of discontinuity There exist epsilon > 0 such that for all delta > 0 there is an x such that |x-0| < delta but |1/(x^2)| >= Epsilon...

Homework Statement Consider a particle in an infinite square well of width
= 1. The particle is in a state given by: Phi=A(1/2-|x-1/2) a=1 b) Find the general form of the expansion coefficients (the Fourier coefficients, right?) for expanding the function in terms of the...

Homework Statement a) Determine the points where the function f (x) = (x + 3) / (x^2 − 3x − 10) is discontinuous. Then define a new function g that is a a continuous extension of f . b) Determine what value of the constant k makes the Piecewise function { (x − k)/ (k^2 + 1) ...

Is there a real-valued function which is discontinuous everywhere, but which has a limit at every point in it's domain? My intuition is that this couldn't occur because, if the limit exists at some x, then it must become "increasingly continuous" in the vicinity of x (otherwise we could find...

/x/ = y is non removable discontinuity x but is /x/^2 = y is a removable discontinuity or not? and why? x^2

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...

Homework Statement Find the numbers, if any, where the function is discontinuous. f(x) = [[x - 2]] The attempt at a solution function is discontinuous for all integer values of x. I know that this is the obvious answer, however I am required to explain this in clear mathematical...

The band gap discontinuity in DFT? Hi everybody... I've read about the band gap problem of Density functional theory, there is a discontinuity of the band gap when an electron add to the Kohn-Sham system I have two questions could anybody answer me? please 1- why this discontinuity happens...

Prove that (0,0) is the point of discontinuity for the function

Homework Statement Give an example of a function f and g such that both are discontinuous at some value c in the Reals and a.)the sum f+g is continuous at c b.)the product fg is continuous at c Homework Equations ... The Attempt at a Solution I have no idea as to how in the...

Homework Statement X, Y are metric spaces and f: X \rightarrow Y Prove that f is discontinuous at a point x \in X if and only if there is a positive integer n such that diam f(G) \geq 1/n for every open set G that contains x Homework Equations diameter of a set = sup{d(x,y): x,y...

Homework Statement suppose that f is bounded on [a,b] and that f is continuous at each point in [a,b] with the exception of x0 in (a,b). prove that f is integrable on [a,b]. Homework Equations f is continuous on [a,x0] and [x0,b] The Attempt at a Solution intuitively, i know that...

Hi all, My first message here. I had the following question in a quiz: For each of the following determine all x values where the function has a removable or non-removable discontinuity and identify whether the discontinuity is a hole, jump or vertical asymptote. 1. f(x) = |x - 3|...

Homework Statement use the definition of continuity to find the values of a and c for which the function F is continuous at x = 1 \[f(x) = \left\{\begin{matrix} 2x-1 & x < 1\\ a+c & x = 1 \\ 3ax^2 & x > 1 \end{matrix}\right.\] Homework Equations The Attempt at a Solution I know the...

Homework Statement y = sqrt(25-x^2) -5<x<0 y = -sqrt(25-x^2) 0=<x<5 dy/dx= -x/y Why is this not a solution on(-5,5) when... y = sqrt(25-x^2) y = -sqrt(25-x^2) are solutions? kinda confused... Could someone explain to me step by step how to solve this...I spent an hour trying to...

Homework Statement 1.Find a function f : R → R which is discontinuous at the points of the set {1/n : n a positive integer} ∪ {0} but is continuous everywhere else. 2. Find a function g : R → R which is discontinuous at the points of the set {1/n : n a positive integer} but is continuous...

We know that matter is discrete, and energy is quantized, (and more quantized things I don't know about.) There is also Planck length? and Planck time? Is spacetime continuous? If we don't know yet, I sure hope it is, because I much prefer to imagine discrete matter and energy interacting in...

Hi, Does anybody know how to identify the exact place where Balmer discontinuity occurs? Does the place of occurence shift towards longer wavelengths for stars with high electron density?

Hello, I am trying to prove the following... lim (x+3) \left|x+5\right|/x+5 x\rightarrow-5 from the left, L=+2 from the right, L=-2 I used delta-epsilon on the right hand limit and got \delta = \epsilon However, I'm not sure how to proceed when I get to this step while trying to prove the...

i am looking for a simple definition of discontinuity using the example 3/(x^2+x-6)

Dirac function :( Hello everyone... I have some triple with my PDEs course especially with the Dirac function. How can I prove it is discontinuous function? I do not know where can I start... Could somebody help me, please.

Hello! I got something that do not understand Here is a picture: Why this function is not differentiable in x=0 ? It can be seen that the slopes of both sides of the function are same? Why it is not differentiable at x=0? Thanks in advance.

Homework Statement Create one example of a function within the context of a real-world science application (i.e., physics, biology, chemistry, etc.) that contains an oscillating discontinuity, Homework Equations y=sin (1/x) The Attempt at a Solution I would like to use the...

Homework Statement f is a function with the property that every point of discontinuity is removable. There are infinitely many such points in f's domain. Define g(x) = \lim_{ y \to x } f(y) . Prove g is continuous The Attempt at a Solution I wanted to maybe conclude something from showing...

hi, So i have a few questions and i can't seem to wrap my head around it. Q1 Decide which of the following functions has a removable discontinuity at a, and then if it is so..remove the discontinuity. f(x)=3[x]; a=-1. (I don't think there is a removable discontinuity because...

What is the point of discontinuity? ex. does x3+x/x have a point of discontinuity at x=0? if there is a discontiuity, is it it removable or not

Hi all, I couldn't find any proof of the following statement: The Fourier series expansion of f(x), which has a discontinuity at y, takes on the mean of the left and right limits i.e. f(y)= (1/2)(f(y+)+f(y-)) is there anyone who can help me? Thanks

Homework Statement Prove that if f:X -> Y is a discontinuous bijection then f-1:Y -> X is also discontinuous. Homework Equations N/A The Attempt at a Solution The contrapositive of this statement is that if f-1:Y -> X is continuous then f:X -> Y is continuous. Since f is...

evaluating a limit--removable discontinuity? Homework Statement I am evaluating the limit of a vector valued function, and one of the pieces I must evaluate is the limit as t approaches 1 of ln(t)/(t^2 -1). I graphed this function on my calculator, and it seems to me that there is a...

If an odd function has an infinite discontinuity in its domain, can it be integrated (such that a convergent finite emerges) with that domain included? For example: \int_{-1}^2 \frac{1}{x^{-3}} dx. Intuitively, it can be simplified to \int_1^2 \frac{1}{x^{-3}} dx and thus the infinite...

Homework Statement I am given the following function, piecewise: f(x) = (-x+b) (x<1) 3 if x=1 (-12/(x-b))-1 (x>1, x=/b) I am asked: 1) For what value(s) of 'b' does 'f' have a removable discontinuity at 1? 2) For what...

Homework Statement Find all values x=a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. f(x)=[x^2-4]/[x-2] Homework Equations The Attempt at a Solution ok the first thing I did was factored out: (x+2)(x-2)/(x-2), then I...

i wondered at the idea that calculus works for continuous functions and in reality fundamental quantities are discontinuous. For example energy or an electron can't asume all values. Therefore isn't there a conflict when we work on a equation like dE/dt or something similar which involve...

[SOLVED] Sequence proof for discontinuity Homework Statement Given a function h(x) = x for all rational numbers x and h(x) = 0 for all irrational numbers, prove that h(x) is continuous at the point x=0 and nowhere else. Homework Equations A function is continuous at a point x0 if and...

Homework Statement I would like to prove that {d \over {dx}} \sigma(x)=2\delta(x), where \sigma(x>0)=1 \sigma(x=0)=0 \sigma(x<0)=-1 Homework Equations The Attempt at a Solution I think that I need to show that \int_{-\infty}^{\infty}{d \over {dx}}...

What do geophysicists mean by depth variation in the shear wave anisotropy of the Lehman discontinuity? And why is there none under the oceans but some under the continents?

Homework Statement 27. limit as x head towards infinity of xsin(1/x) is A 0 B infinity C nonexistent D -1 E 1 from barron's ap calc 7ed, Chapter two review questions p.37 how come the answer is E? Isn't it A b/c the limit equals infinity or neg infinity times zero? the Book explains...

As part of a separable solution to a PDE, I get the following ODE: X''-rX=0 (*), with -infty<x<infty and the boundary condition X(+/-infty)=0 (X is an odd function here). Thus I have assumed r>0 to avoid the periodic solution, cos. I, therefore, argue that the solution is the symmetric...

the book says that g(x)= x ,if x is not equal to 2 / 1,if x=2 has a removable disc. at x =2. I couldn't remove it.I guess I didn't understand a removable dic. completely.I have an exam on friday.I need your help:confused...

I have been doing some function questions. I think it is Calculus because it is in a Calculus course; however, it could be pre-calculus. I decided to post it here anyway. Question: (x+5)(x+4) ___________ (x+4) Every question I have done involve a POD like this. Two on the top and one...

I have a test tomorrow and this is a subject we only briefly touched on. I can find points of discontinuity graphically very easily, but I have no idea how to find them algebraically using just the equation. I know that when the denominator = 0 and in most piecewise functions there is...

How can i find the discontinuitys of \frac{3x+1}{\ x^2+7x-2} without a calculator? This is an even numbered homework question to which the teacher says he won't help us and there is no answer in the book, plus we are not allowed to use calculators.

just a basic question, so if I'm asked to find 2 functions that are discontinus, but when added together, becomes continuous, how do I approach that? can I say like, let F(x) = 1 for x =< 0, and f(x) = 0 for x > 1. G(x) = 1 for x =<0 and g(x) = 0 for x = 1. can I just somehow "add" f...

what is the definition for discontinuity? I got a question on a math test wrong because it asked to "justify your answer" but I couldn't because I didn't know the definition for discontinuity.