Interval Definition and 712 Threads

I am working on a homework problem, and because it is a homework problem, I will not tell you the specifics or ask for an answer. My question has very little to do with the problem in particular, I just wanted to make that disclaimer. Oh, and the derivation of the Lorentz transformation was NOT...

just a cool fact I thought I'd share with anyone who's interested: The set of real values functions on any interval in R has cardinality at least 2^c. Pf: Consider characteristic functions defined on the interval, (a,b). (Note: a characteristic function is a function that can be defined...

I am working with a linear line with positive slope, the points are given. 1. In interval notation write for which values f(x) > 36 2. At f(x)=36 x=21 3. I think it should look like (-inf,21)

Easy Question but can't seem to make head way on this one! For the Function shown in the link below find and plot f(2 -t/2) http://www.imagedump.com/index.cgi?pick=get&tp=516020

Homework Statement A ball is thrown downward with initial speed of 8m/s from a height of 30m. Homework Equations \After what time interval does the ball strike the ground The Attempt at a Solution acceleration will equal -9.8m/s^2 because it's free fall would i use equation...

1. Find the domain of the function 5x/8x^2+9 in interval notation. 2. 3. I believe the domain is all real numbers, but do not know what that would look like in interval notation. Could someone show me?

Can anyone explain exactly how the diagram in Schutz 'Invariance of the interval' actually shows the rod appears the same length in the two different frames and how in any case that shows the direction of the relative velocity between two frames is irrelevant? I can see that the worldline of...

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...

I am given the four-vector of two events in a reference frame S and I found that they are spacelike. I want to then find the reference frame in which these two events are simultaneous. I am still a bit confused about how this is even possible. There is that equation: gamma * delta t' =...

Find an open interval about a on which the inequality | f(x) - L | < E holds. Then give a value for D > 0 such that for all x satisfying 0 < | x - a | < D the inequality | f(x) - L | < E holds. f(x) = x^2, L = 4, a = -2, E = .5 To solve I setup the inequality Step 1: -.5 < x^2 - 4 <...

When an object is traveling at c the spacetime interval is zero. I can follow the algebra that gets to this conclusion. Is there a conceptual, mentally conceived image, explanation for a spacetime interval of zero ?

Homework Statement Find the radius of converge of: \sumx^{}(n choose k) Homework Equations Radius of converge = 1/limsup|an+1/an|, for power series: anx^n The Attempt at a Solution Tried rewriting (n choose k) as: n!/[k!(n-k)!] but where do I go from...

Is ther any form by bisection or simiar to obtain a partition for an infinite-dimensional interval (aka functional space)?? i believe you could obtain a partition for every interval 'centered' at a certain function as: X(t), X(t)+\delta (t-t`), X(t)+2\delta (t-t`), X(t)+\delta (t-t`), ...

[Solved]Is a stats question,just need some clarity on it-"total width of less than 2. Homework Statement Hi.The result of a memory test is known to be normally distributed with mean mew and standard deviation 1.0. It's required to have a 95% confidence interval for mew with a total width of...

Hi all, I'm having difficulty proving that all intervals of the real line are connected in the sense that they cannot be decomposed as a disjoint union of two non-empty open subsets. Here is the "proof": Suppose X is an interval and X = (X intersect U) union (X intersect V)...

Hi... I know that this question will be found little bit stupid, but unfortunatly I can't see where I made a mistake. Let's have stick with light sources on both ends. In stick's reference frame the flashes from both sources are simultaneous. In laboratory ref. frame they are not. However...

How do we prove that the spacetime interval is invariant? Also why is it so important?

Homework Statement Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart. What is the time difference between the two events in this second inertial system? Homework Equations...

(Moving this to another section, because it is not for a particular course ...) I'd greatly appreciate any direction toward establishing the result below. I am studying statistics on my own, and found this in some online materials, but it didn't come with a solution, and I've been a bit...

I hae built a MK111 variable interval timer http://www.maplin.co.uk/Module.aspx?ModuleNo=25224&criteria=TIMER%20KITS&doy=6m1" and intend to use it for a free-flight glider which is a university project! I wish for the timer to power an electric motor for 2sec and then pause for a desired...

i find in the literature in different textbooks the term proper time Thomas A. Moore, Six Ideas that Shaped Physics (McGraw-Hill) 1998 and the term proper time interval Yuan Zhong Zhang, Special Rekativity and its Fundamental Foundations, (World scientific ) I consider that the first is...

Homework Statement Find the absolute max and min of h(x) = cos(2x) - 2sinx in the closed interval [(pie)/2, 2pie] The Attempt at a Solution I got h(x) = cos(2x) - 2sinx h'(x) = -sin(2x)*2 - 2cosx <---chain rule i did :smile: 0=-2sin(2x) - 2cosx 0=[-2sin(2x)/-2] -...

Ok i know it should be because it has the same cardinality as R and R is uncountable. But take for example (0,1). Heres a method I would use to count all its elements: 0.1,...,0.9 0.01,...,0.99 0.001,...,0.999 . . . 0.(n-1 zeros)1,...,0.(n 9's) . . . so count starting from the top...

I need help finding the radius & interval of convergence of the following power series: The sum from n=0 to infinity of... (2-(n)^(1/2)) * (x-1)^(3n) I think the ratio test is supposed to work, but I narrow the limit of the test down to 1/|x-1|^3 < 1, and this doesn't make sense to me. Is...

I just wanted to see if someone could verify my answers: \\sum_{n=0}^\\infty \\frac{(x+7)^n}{sqrt(n)} I get: -8<x<-6 \\sum_{n=1}^\\infty \\frac{(-1)^n*x^2n}{n!} This one I'm not sure of. When I take the limit I get 0. When I solve the inequality I get x. I can't find an...

an object is generally categorized as either a plant, an animal, or a mineral. is an interval of time (for example, 11/12/2006 at 00:52 (UT) thru 11/13/2006 at 00:51 (UT), here in burbank, california) an object, and if it is, how should it be categorized? thanks!

The question I'm currently working on now is to find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x-2cosx, [-pi, pi] f'(x) = 1+2sinx = 0 From here I've found that -30 degrees(-pi/6) and -150(-5pi/6) degrees are the two intercepts in the equation...

A. Einstein states in The Principle of Relativity, pp 111 - 112: "The modification to which the special theory of relativity has subjected the theory of space and time is indeed far-reaching, but one important point has remained unaffected. For the laws of geometry, even according to the...

Hi, I have a problem that says to solve this equation for the interval 0<theta<2 pie which is one revolution of the unit circle. The equation is: (square root of 2)(cos 2theta) = 1 The cos2theta is a double angle, but I couldn't find any solutions for theta that would = 1 at the end. The...

When a question asks along the lines of : "If a function (g) is decrasing on the interval {x,x)...What would the limg'(x) be (As it approaches infinity)" What are they looking for? and whatequation am I using? I'm not looking for too much info on how to do, but which direction should I go...

Hi I have this series here \sum_{n=1} ^{\infty} \frac{1}{x^2+n^2} I need to show that the Radius of convergens R = \infty and the interval of convergens therefore is (- \infty, \infty) My question is to do this don't I use the ratio-test? Sincerely Yours Hummingbird25

Just what the title says. In the book Spacetime Physics, by Taylor and Wheeler, the time coordinate is measured in metres of light-travel time, but that's just a roundabout way of saying that they are using the second...or am I missing the point. :blushing:

Hi, I was wondering if there was a way to prove the invariance of the space-time interval just from postulating a constant speed of light and an isotropic space-time. Most arguments go "from the Lorentz transformations it can be seen that the interval is invariant." Can we show the...

am trying to find the intervals of convergence for the summation, first deritive, and intergral of problems like this: the sum of [(-1)^n+1(x-5)^n]/[n5^n] from n=1 to infinity i know it is an alternating series and thus i am attempting to use that test to find convergence/diverigence lim...

Hello everyone, I'm confused (as usual). I think i found the radius of convergence but then waht do i do to find the interval on which it converges? The directions says: Find all the values of x such that the given series would converge...

Can somebody explain to me how to get the acceleration in the second and third interval please. A car starts from rest and accelerates uniformly for 10.0s, reaching a speed of 20.0m/s. It then continues traveling at that speed for 40.0 additional seconds before decelerating uniformly and...

(A, B) is an interval in the real line. If I take the middle point (B-A)/2, and then take the middle point of each of the two subintervals of (A,B), and then take the middle point of each of the four subintervals of (A, B) and I go on this indefinitely, can I be sure that sooner or later I will...

\int^{6}_{0} \sqrt{1-n^2x^2}dx=\pi+e I need to solve this for n. I believe there should only be one possible function of the form y=x^n that gives an arclength of \pi+e over the interval x=0 to x=6, and wish to find the value of n that such a function must have. Does anyone know how to do...

A friend had a question about Interval Notations, I had no idea how to do it..but kind of ..well tried to learn how. And I think the answer is A? Any help here? 1: Write in interval notation: | x | ≤ 3 a. (-∞, -3] U [3, ∞) b. (-∞, ∞) c. [-3, 3] d. No solution

could someone give me a hand with this please? i need to use the interval halving method to show that the function f has a root in the interval [a,b]. I need to approximate that root and determine a bound on the error of my estimate. f(x)=x^3+2x^2+pi(x)-(square root of 2) I have...

I need the following proposition in order to prove another theorem, and I can't seen to find it in my textbook. Any hints on how to proceed, or whether it's actually TRUE, would be helpful. "If f is defined and continuous on some interval I, then there exists subintervals I'=[x-a,x+b], for...

I've tried all the possible ways I could think of to tackle this problem, but found no satisfactory answer. I would like to show that \lim_{\epsilon \rightarrow 0} (t-\epsilon, t+\epsilon) = \{t\} Is it possible?!

I'm suppossed to find the average acceleration of the mass during the time interval from -t to t. The formula I'm using is a(-t,t)=\frac{(v(t)-v(-t))}{(t-(-t))} I've already derived v(t) and v(-t) but I'm not sure how to simplify them after subtracting them. v(t)=-R\omega sin(\omega...

A formula of prime numbers for interval (q; (q+1)^2), where q is prime number. Let: Q_k – the multitude of first k prime numbers to some extent: Q_k = (q_0 = 1^0, q_1 = 2^n1, q_2 = 3^n2, q_3 = 5^n3, q_4 = 7^n4, … q_k = u^nk) (here the expression «_i» signifies lower index, and «^ni»...

Alright this is confusing me a bit... Find k so that the following function is continuous on any interval? f(x)=kx if 0 \leq x \leq 2 and f(x)=5x^2 if 2\leq x Alright I know the answer is 10, but I don't understand how you get there I mean I just doubled 5, because I took it off...

Hi, I am an 3rd engineering student working on my coop report. My job was to design routes for survey work, and come up with figures of potential time savings if this was to be done on a grand scale. The sites are divided into 15 regions (by geography) but are not in any particular order...

Let D[a,b] be the set of piece-wise continuous functions on the close interval [a,b]. Show that D[a,b] is a subspace of the vector space P[a,b] of all functions defined on the interval [a,b]. Can someone get me started? Do I just need to show that they are closed under addition and...

What is the 95% confidence interval for 100 ohm resister with 10% tolerence? Here is my work so far, can someone please tell me if I am doing it wrong or right? Thank you in advance. from table 95%: k = 1.96 100 * 0.1( which is the 10% tolerance) = 10 10 / sigma >= 1.96 Sigma <=...

Hi, I am trying to prove the nested interval theorem for R^n. It is stated as follows: Let (K_i : i in N) be a decreasing sequence of bounded closed sets in R^n and each K_i is non empty. Then the intersection of all K_i for i in N is not empty. This is what I have so far: Since...

I*m looking for some help with a statistics question: Builder A and Builder B both take random samples of nails, and the width of the nails are measured in centimetres - Builder A estimates that a 95% confidence interval for the width of the nails is 1.2 +/- 1.96 * 0.05. Builder B estimates...