Continuous Definition and 1000 Threads

The energy and the power contents of a signal x(t), denoted by E_x and P_x, respectively, are defined as (1) E_x = \int ^{\infty}_{-\infty} |x(t)|^2 dt (2) P_x = lim_{T\rightarrow \infty} \frac{1}{T} \int ^{T/2}_{-T/2} |x(t)|^2 dt Let us use the discrete time (sampled) signal, with sampling...

I'm having a trouble doing this kind of problems :S Lets try this for example: The joint p.d.f of the continuous random variable X and Y is: f(x,y)= (2y+x)/8 for 0<x<2 ; 1<y<2 now we're asked to find a probability, say P(X+Y<2) I know i have to double integrate but how do I choose my...

The probability density function of the time customers arrive at a terminal (in minutes after 8:00 A.M) is f(x)= (e^(-x/10))/10 for 0 < x c) Determine the probability that: two or more customers arrive before 8:40 A.M among five that arrive at the terminal. Assume arrivals are...

Why is it that we assume electric potential to be continuous across boundaries in electrostatics problems (like, say we have a situation with concentric spheres with different equations for electric field across boundaries)? This is the case as far as I've seen at least. I am in introductory E&M...

Hi all, I have a question relating to the sum of continuous random variable probabilities that I hope you can help to answer. In any probability density function (pdf), dealing with discrete or continuous random variables, the sum of the probabilities of all possible events must equal 1...

Homework Statement (This is my first post and I'm not sure why the Tex code isn't working, sorry).Suppose fis a positive continuous function on [1,0] .For each natural numbern define a new functionF_n s.t. F_n(x) = \int_0^1 t^ne^{xn}f(t)dt (a) Prove that lim_{n\to\infty}F_n(x) = 0 for...

Transition from bound states to "continuous" states If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a...

"Continuous eigenstates" vs "discrete eigenstates" There's this thing that's bothering me: if I have an Hamiltonian with a discrete and continuous spectrum, every book I read on quantum mechanics says that eigenvectors of discrete eigenvalues are orthogonal in the "Kronecker sense" (their...

Homework Statement You're simply given f(x)/g(x) and it asks, when is the function continuous? There was one that was definitely wrong, so I remember these remaining choices: a) It is continuous when f(x) and g(x) are defined b) " " when g(x) cannot equal 0 c) " " when g(x) is defined...

Homework Statement Consider a linear system dx/dt = Ax of arbitrary size. Suppose x1(t) and x2(t) are solutions of the system. Is the sum x(t) = x1(t) + x2(t) a solution as well? How do you know? Homework Equations The Attempt at a Solution I have no idea how to go about this...

Whats the difference between a discrete time impulse and a continuous time impulse signal ?

a vehicle driver gauges the relative speed of the next vehicle ahead by observing the speed with which the image of the width of that vehicle varies. This speed is proportional to X, the speed of variation of the angle at which the eye subtends this width. According to P. Ferrani and others, a...

Homework Statement Is t^2, -2t and 2 continuous on an open interval? Homework Equations I have re read the theorems and explanations of how something is continuous but i still don't understand it. The Attempt at a Solution

Hello friends, I am quite confused how an absolute function is called a continuous one. f(x) = |x| has no limit at x=0 , that is when x > 0 it has a limit +1 {+.1, +.01, +.001} and -1 when x <0 {-.1, -.01, -.001} that is the reason it's not differentiable (left and right side limits are not the...

Could you please check the statement of the theorem and the proof? If the proof is more or less correct, can it be improved? Theorem Let be a topological space and be the discrete space. The space is connected if and only if for any continuous functions , the function is not onto...

I was reading a Ph.D. thesis this morning and came across the claim that "a uniform limit of absolutely continuous functions is absolutely continuous." Is this true? What about the sequence of functions that converges to the Cantor function on [0,1]? Each of those functions is absolutely...

Homework Statement Find an example of a continuous function f:R->R with the following property. For every epsilon >0 there exists a delta >0 such that |f(x)-f(y)| <epsilon whenever x,y e R with |x-y|<delta. Now find an example of a continuous function f:R->R for which this property does nto...

I have spent ages on this final part of a question but don't seem to be going anywhere - any help would be greatly appreciated! Given a function f:R->R let X be the set of all points at which f is continuous. Find an example of a function defined on R which is continuous on Z only.

I was studying particle in a box from shankar and I couldn't get the following point. If V is infinite at for x > L/2 and x < L/2, so is double derivative of psi. Now Shankar mentions that it follows the derivative of psi has a finite jump. I am not able to get this point because according to my...

When you combine general relativity and quantum mechanics theory, does time become quantised? Or are there any theories where this is a possibility? We're doing both special relativity and quantum mechanics at the moment, in different modules, both lecturers make passing references to the...

Homework Statement From 2.2 Worked Examplehttp://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/continuous-mass-flow/MIT8_01SC_coursenotes19.pdf" Emptying a Freight Car - A freight car of mass mc contains a mass of sand ms At t = 0 a constant horizontal force of...

Hello. I have to find the Fourier series for f(x) = 1 + cos(pi x / L). My question is about f(x) Is this function even? I plotted it out and it looks even. The question I am completing starts off by saying: assume that any function f for which f and its derivative are piecewise continuous...

If f is a continuous functional on a normed space, do you have \sup_{\|x\| < 1} |f(x)| = \sup_{\|x\| = 1} |f(x)| If so, why? If not, can someone provide a counterexample?

f uniformly continuous --> finite slope towards infinity Homework Statement Given f:R \rightarrow R uniformly continuous. Show that \limsup_{x\rightarrow \infty} \displaystyle|f(x)|/x<\infty i.e. \exists C \in R: \, |f(x)|\leq C|x| as x \rightarrow \pm \infty. Homework Equations The...

Hello guys, I tried to figure this out and I got my answer. I just want to check it. So would you guys please help me with it? Thank you! Here is the question: A nonconducting rod of length 2a has a charge Q uniformly distributed along it. Find the expression for x-component of the electric...

Homework Statement Let f be a real-valued function defined and continuous on the set of real numbers. Which of the following must be true of the set S={f(c):0<c<1}? I. S is a connected subset of the real numbers. II. S is an open subset of the real numbers. III. S is a bounded subset of the...

If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous? I am very confused, can someone offer some explanation? Any input is greatly appreciated.

I'm trying to understand the set C_0(X), defined here as the set of continuous functions f:X\rightarrow\mathbb C such that for each \varepsilon>0, \{x\in X|\,|f(x)|\geq\varepsilon\} is compact. (If you're having trouble viewing page 65, try replacing the .se in the URL with your country domain)...

Homework Statement let f be the function defined in the region |z|<1 , by f(z)=z^5. prove that f is uniformly continuous in |z|<1...where z is a complex number Homework Equations The Attempt at a Solution

Homework Statement Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space. Homework Equations By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon The Attempt at a Solution...

Is it possible to have the following signal: 1) Discrete and analog 2) Discrete and digital (I believe this one is true and very common in man made product) 3) Continuous and analog (I believe this one is also true and very common in nature) 4) Continuous and digital If a picture...

X is a random variable with a continuous distribution with density f(x)=e^(-2|x|), x e R How would you calculate E(e^(ax)) for a e R? Will it be right to take a certain range of a? And also, can you take the bounds for the integral to be between -Infinity and Infinity?

Homework Statement Let (X,d) be a metric space and let {x_n} be a sequence in X converging to a. Show that d(b, x_n ) ->d(b,a) Homework Equations The Attempt at a Solution For every eps > 0 there is an N such that d(x_n,a) < eps for all n>= N But where do I go from here...

Question Let (S; d) and (T;D) be metric spaces. A function f : X -> Y is said to be uniformly continuous if ( for all epsilons > 0)(there exists a sigma > 0) such that d(x; y) < sigma => D(f(x); f(y)) < epsilon a. Show that a uniformly continuous function maps Cauchy sequences to Cauchy...

Hello, I have a Mathematica code with Manipulate [] and a number of inputs. At the end I have ContinuousAction->False, but my code keeps repeating the evaluation, even when the inputs are not changing. Ideally, I would like it to evaluate once when an input is changed. But now it goes like...

Homework Statement Find a function f that has a continuous derivative on (0, ∞) and that has both of the following properties: i. The graph of f goes through the point (1, 1) ii. The length L of the curve from (1, 1) to any point (x, f(x)) is given by the formula L = lnx + f(x) - 1...

I'm very sorry for the initial post - I was having trouble working with LaTex (I've never used it before and the preview post wasn't showing me what I had expected it to look like - it kept giving me a square root symbol for every code). Find the electric field a distance z above the centre of...

Do everywhere continuous, nowhere differentiable functions realistically model anything in physics, chemistry, or biology ? Do such functions have applications to those sciences ?

Prove that any f: D -> C(complex) which is holomorphic in D subset of C is continuous in D f is holomorphic in D if it is differentiable at every c element of D. A function is differentiable at c if lim(h->0) (f(c+h) - f(c))/h exists. I know from reals that a function is only...

Homework Statement Let (X,T) be a normal topological space. Let R be the ring of continuous real-valued functions (with respect to the given topology T) from X onto the real line. Prove that the that T is the coarsest Topology such that every function in R is continuous. Homework...

Homework Statement Let O be an open subset of R^n and suppose f: O --> R is continuous. Suppose that u is a point in O at which f(u) > 0. Prove that there exists an open ball B centered at u such that f(v) > 1/2*f(u) for all v in B. Homework Equations f continuous means that for any {uk} in O...

If we suppose a > 0 is some constant and f: R \rightarrow R is f(x) = |x|^a sin(1/x) if x \neq 0 and f(x) =0 if x=0 if we let F(x) := f '(x) for x \neq 0 and F(0) :=0. For what values of a is F a continuous function in R

Homework Statement three functions: y=\begin{cases}\arctan \frac{1}{x}\ x\neq0\\ 0\ x=0\end{cases} y=\frac{1}{x}, y=|x^2-1| and what about inflection point? The Attempt at a Solution first function is concave on left of 0, convex on right, so from definition it should be inflection point...

I have about 40 tabs open on this right now and something important is slipping my grasp. I know this has been covered a million and a half times, but for some reason I cannot seem to find a straight answer (or more probably realize and understand it when I see it). When I take the Continuous...

Homework Statement Find the continuous points P and the differentiable points Q of the function f in {R}^3, defined as f(0,0,0) = 0 and f(x,y,z) = \frac{xy(1-\cos{z})-z^3}{x^2+y^2+z^2}, (x,y,z) \ne (0,0,0). Homework Equations The Attempt at a Solution If you want to look at the limit I'm...

Homework Statement Find A and B so that f(t) is continuous everywhere. Homework Equations Suppose that: [PLAIN]http://img690.imageshack.us/img690/8531/eqwkshp3.png The Attempt at a Solution Well, I wouldn't be posting if I wasn't lost, but I will tell you what I've tried. I know that I...

1. Prove f is differentiable at x=xo implies f is continuous at x=xo using epsilon and delta notation. 2. I have gotten this far: absolute value(f(x)-f(xo)) <= absolute value(x-xo)*(epsilon + absolute value(f '(xo))) <= means less than or equal to. 3. I need to get here: absolute...

Hi Guys, I've used this forum as a great resource for a while now and it's always helped me out. Now I'm really stuck on something and was hoping you guys could help out. It's a pretty long question, but if you guys can just give me a general direction of what to do, I can go ahead and work it...

1. Homework Statement find all points that are continuous in the function f f(x,y) = (y-5)cos(1/x2) if x not = 0 if x = 0, then f(x,y) = 0 3. The Attempt at a Solution my notes says that to show continuity, i must show that f(x,y) = f(a,b) when x,y tends to a,b how do i do that...

Homework Statement How would I demonstrate that a function is continuous? Would I just show that it's derivative exists? Thanks for the help.