Continuous Definition and 1000 Threads

Hello, I have this exercise that I can't solve: when x<3 the function f is given by the formula f(x)=$\frac{4{x}^{3}-12{x}^{2}+10x-30}{x-3}$ when 3 < or =x f(x)=$3{x}^{2}$-2x+a What value must be chosen for a in order to make this function continuous at 3? I think that I will have to equate...

We know differentiability implies continuity, and in 2 independent variables cases both partial derivatives fx and fy must be continuous functions in order for the primary function f(x,y) to be defined as differentiable. However in the case of 1 independent variable, is it possible for a...

Hi! (Wave) Find the cardinal number of $C(\mathbb{R}, \mathbb{R})$ of the continuous real functions of a real variable and show that $C(\mathbb{R}, \mathbb{R})$ is not equinumerous with the set $\mathbb{R}^{\mathbb{R}}$ of all the real functions of a real variable. That's what I have tried: We...

For a definite particle,the decay mode is determinant,finite kind,which embody the characteristic of quantum mechanics. But for a specific mode of a definite particle's decay,the decay spectrum,ie,energy of products,continuous,or discrete? Decay is a process which has unique initial...

I'm an Arduino electronics hobbyist I'm not a professional electrical engineer. How would I mount a small ultrasonic sensor on a continuous rotation servo, without tangling the wires? How would I fix this problem easily and what's the most common way to mount electronics in a rotating object...

Let's see if I have this straight: Observables are represented by Hermitian operators, which can be, for some appropriate base, represented in matrix form with the eigenvalues forming the diagonal. Sounds nice until I consider observables with continuous spectra. How do you get something like...

I'm really stumped on how to do these proofs… I would really appreciate any help or insight!

Let $f: K\subseteq \mathbb{R}^n\to \mathbb{R}$ continuous, $K$ an connexe subset. Show that $f(K)$ is connexe.

When a particle decoheres, or its component states get entangled with the ``environment``, surely this is not a final eigenstate. The particle is interacting ( becoming entangled etc) with other particles and systems constantly. Therefore, isn't decoherence a continuous process?

Hey! :o If $f$ is a measurable complex function (that means that it doesn't take the values $\pm \infty$) with compact support, then for each $\epsilon >0$ there is a continuous $g$ with compact support so that $m(\{f\neq g\})<\epsilon$. Could you give me some hints how I could show that...

Can we judge about continuity of function x/sinx?? Many examples in Google about sinx/x or xsinx but nothing about this function? Is there any special case? Regards

Homework Statement Let X denote a continuous random variable with probability density function f(x) = kx3/15 for 1≤X≤2. Determine the value of the constant k. Homework Equations I'm not sure if this is right but I think ∫kx3/15 dx=1 with the parameters being between 2 and 1, The Attempt at a...

Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...

Hi, friends! Let ##f:[a,b]\to\mathbb{C}## be an http://librarum.org/book/10022/173 periodic function and let its derivative be Lebesgue square-integrable ##f'\in L^2[a,b]##. I have read a proof (p. 413 here) by Kolmogorov and Fomin of the fact that its Fourier series uniformly converges to a...

GR models of the universe describe it as a continuum, a smooth manifold, on the other hand the universe contains matter and matter is considered discrete.

Homework Statement Show that if F is an antiderivative of f on [a,b] and c is in (a,b), then f cannot have a jump or removable discontinuity at c. Hint: assume that it does and show that either F'(c) does not exist or F'(c) does not equal f(c). 2. The attempt at a solution I attempted a proof...

Homework Statement Given the piecewise function f(x) = \left\{ \begin{array}{lr} \frac{(2-x)^2-p}{x} &: x < q\\ r(x+6) &: q \leq x <2 \\ x^3-p &: x \geq 2 \end{array} \right. Find the values of p,q,r such that f(x) is continuous everywhere and f(2) = p The Attempt at a Solution Since f(2)...

Homework Statement A function f is defined as follows: ƒ(x) = sin(x) if x≤c ƒ(x) = ax+b if x>c Where a, b, c are constants. If b and c are given, find all values of a (if any exist) for which ƒ is continuous at the point x=c. Homework EquationsThe Attempt at a Solution I was unsure of how to...

Find the values of a and b that make f continuous everywhere. f(x) = (x2 − 4)/(x − 2)...if x < 2 ...ax2 − bx + 3... if 2 ≤ x < 3 ...4x − a +b....if x ≥ 3 This is a piece-wise function. So I know that to be continuous everywhere, the function has to be one solid line. But I have no idea how to...

Hello So from what I understand, the continuous compound formula finds out the most you can get from interest no matter how many times you compound the interest in a set amount of time. So how come when I plugin in a big number into the regular compounding formula for the rate, the end amount...

I need to purchase a device that will push something forward and backward continuously, in order to make wings flap like a bird. Linear actuators seem to be the right thing to buy, except these require pressing buttons to go forward and then back. What can I buy/what can I do that will allow a...

I've actually been through Plovdiv. The area is quite interesting. I would love to visit Turkey, and Lebanon and Syria, once is becomes stabilized. https://www.yahoo.com/travel/the-oldest-cities-in-the-c1412019813265.html

If a function is continuous (nothing else specified), is it defined over R? Continuity means a function's value being the same as the limit for that point IIRC, but I don't know if it being continuous (over R presumably) means that it is also defined over R, or just that it's continuous wherever...

dear all, the virtual work pinciple can be used to derive the equilibrium equations for the mechanical systems. however, when I want to apply it to a continuous system, I found it can not give out the simple equilibrium equations. there should be something wrong with my thinking. I expect some...

Homework Statement u(x) = \begin{cases} \frac{3x+b}{4} & \text{if } x \geq 2 \\ \frac{(3-x)^n-a}{x-2} & \text{if } x < 2 \end{cases} find the value of a and b for which the function is continuous at 2 The Attempt at a Solution I tried to proof that lim(3x+b)/4 = lim (3-x)^n-a/x-2 = f(2)...

So, the exercise is to find the expected value of following distribution: f(x) = 0,02x 0<x<10 answer in the book says 6,67 As far as I knowe, the expected value is calculated by the Integral of x * f(x) between 0 and 10, in this case! It looks like this won't give the result 6,67! what am...

I am not sure if I recall all the ways for a symmetry to appear as some particle in a Quantum Field Theory. - The Lagrangian and the vacuum is invariant under the generators of a global symmetry/gauge group. Then the particles in the theory are classified according representations of such...

Doubtless you are all familiar with a rail gun made by using permanent magnets. An example is given here: http://sci-toys.com/scitoys/scitoys/magnets/gauss.html Assuming the railgun could me made curved, won't it be possible to build a curved track to transport the projectile - assume...

I have learned the fact from Peskin QFT book,that one-particle state presents a delta function form in spectral function at s=m^2,while multiparticle states present a continuous form begin at s=4m^2,but i don't really understand the reason.What cause the difference between one-particle state and...

Considering: a) The logical foundation of Mathematics and Mathematics as the foundation of Physics. b) The principle of excluded middle (nothing can be simultaneously something and its opposite). c) The ultimate physical reality: It must be discontinuous or continuous; it can neither be...

Is the tangents function tan(x) continuous when x = 90 degrees or x = pi/2?

Homework Statement A plastic rod of finite length carries an uniform linear charge Q = -5 μC along the x-axis with the left edge of the rod at the origin (0,0) and its right edge at (8,0) m. All distances are measured in meters. Determine the magnitude and direction of the net electric...

I read that in any locally convex topological space X, not necessarily a Hausdorff space but with linear operations continuous, for any ##x_0\ne 0## we can define a continuous linear functional f:X\to K such that f(x_0)\ne 0. I cannot find a proof of that anywhere and cannot prove it myself...

Homework Statement please refer to the question, i can't figure out which part i did wrongly. i 'd been looking at this repeatedly , yet i can't find my mistake. thanks for the help! the correct ans is below the question. where the c= 283/5700 , q = 179/5700 Homework Equations The...

I think this is a theorem, and I'm telling myself that I've proved it. Just a shout out for any possible counter-examples: If a function f(x) is continuous on some interval and has non-zero derivatives at its root(s) (where f(x')=0 ) then there is some interval around the roots where there are...

My question is: Let f:\bigcup_{\alpha}A_{\alpha} \rightarrow Y be a function between the topological spaces Y and X=\bigcup_{\alpha}A_{\alpha}. Suppose that f|A_{\alpha} is a continuous function for every \alpha and that {A_{\alpha}} is locally finite collection. Suppose that A_{\alpha} is...

For discrete variables, a POVM on a system can be thought of as a projective measurement on the system coupled to an apparatus. This is called the Naimark extension. Is this also true for continuous variables? http://arxiv.org/abs/1110.6815 (Theorem 4, p10)

Let's say I'm applying electrical currents to a certain part of a human test subject and measuring certain deflections in his heart readings during this period. Before I increase the electrical currents, which could be dangerous, I'm interested to see if the changes in electrical currents are...

So I've been self-studying from Griffiths Intro to QM to get back in shape for graduate school this fall, and I guess I'd just like some confirmation that I'm on the right track... So while I am sure there are many other applications, the one I am dealing with is eigenfunctions of an operator...

I thought I understood all the theory quite well and sat down to begin coding until I realized that calculating a probability at a point within a normal distribution in the application of bayes' rule you can't simply plug the point into the normal distribution and get the value since the...

Homework Statement A charge lies on a string that is stretched along an x-axis from x = 0 to x = 3.00 m; the charge density on the string is a uniform 9.00 nC/m. Determine the magnitude of the electric field at x = 8.00 m on the x axis. Homework Equations \int_0^3 kλ/(8-x)^2\,dx...

I am watching James Binney's QM lectures on iTunes University, and also going through his free textbook. He is a tough teacher, but I love how many misconceptions he points out, and some of the points he makes are very subtle and mind blowing when the lightbulb comes on. I am confused on...

Consider the following joint probability distribution function of (X , Y): a(x + y^2) {0<=x<=2, 0<=y<=2} 0 otherwise Calculate the value of the constant a that makes this a legitimate probability distribution. (Round your answer to four decimal places as appropriate.) And then, For the...

For the following probability density function: f(x) = [(x^2)/9] between 0 <= x <= 3 0 otherwise calculate the expected value E(X) of this distribution, and also calculate the variance I know I have to integrate the function but I don't know what else. Thanks!

Hello. The question is in the attached, together with my attempt. As you can see, I found the limit, but I don't know what each value means. If I have calculated the limits correctly, how do I know know if f(z) is continuous at 0 or not?

Can someone tell me if the continuous Fourier transform of a continuous (and vanishing fast enough ) function is also a continuous function?

If the discrete summation is symbolized by ##\sum## and the continuous by ##\int##, so, by analogoy, the discrete product is symbolized by ##\prod## and you already thought what is the symbol for the continuous product?

Let f1,...,fN be continuous functions on interval [a,b]. Let g:[a,b] -> R be the function give by g(x) = max{ f1(x),..., fN(x)}. show that g is a continuous function i posted this earlier with one proof, I am trying another more general let ε >0 and arbitrary k. if f1(x) >...> fN(x)...

Hi there! How can I prove that a function which takes an nxn matrix and returns that matrix cubed is a continuous function? Also, how can I analyze if the function is differenciable or not? About the continuity I took a generic matrix A and considered the matrix A + h, where h is a real...

Hello! (Smile) I am given this exercise: $$f(x)=\left\{\begin{matrix} \frac{e^x-1}{x} &, x \neq 0 \\ 1& ,x=0 \end{matrix}\right. , x \in [0,1]$$ Show that $f$ is integrable in $[0,1]$,knowing that if $f:[a,b] \to \mathbb{R}$, $f$ continuous,then $f$ is integrable in $[a,b]$. So,I have to...