Interval Definition and 712 Threads

Given the interval [0,1) is this a good Open cover with infinite subcovers {(An)} such that An =(-1/n, n) with n \in lN Is there any reason we should stay to the boundaries of the set we're trying to cover? I'm thinking that even (-n, n) should work. Am I wrong?

Homework Statement \sum from n=1 to inf (1+ 1/2 + ... 1/n)x^n Find the radius of convergence and the interval of convergence of the given power series. Homework Equations Dunno.. The Attempt at a Solution Stuck thinking about it. I'm not sure if I can combine what's in brackets with the...

Homework Statement Given that note x has frequency 300 Hz. Find the frequency of note y if it is two sext higher than x. Homework Equations sext interval --> x : y = 24 : 40 The Attempt at a Solution I can find the value of y if the interval is sext. x : y = 24 : 40 300 : y =...

Homework Statement Find the solution of the given initial value problem in explicit form and determine the interval in which the solution is defined. \[x dx+ye^{-x}dy = 0\] with initial condition y(0) = 1 Homework Equations The Attempt at a Solution I solved the first part...

Hi, I'm reading a book on SR/Field theories that simply posits the space-time interval and from that defines a Lorentz transform as any transformation which leaves the interval invariant. My question is how do we posit the space-time interval in this manner using only the postulates of...

Given two functions f_{1}(x) and f_{2}(x) that are differentiable on [a_{1},a_{2}] and \int^{a_2}_{a_1}f_1(x)f'_{2}(x)dx=b_2, how would one calculate \int^{a_2}_{a_1}f_1(x)f'_{2}(x)dx? This is not a homework problem. I saw it on the internet and realized that I did not know where to begin...

Homework Statement Two events occur 5 s apart in time and 3 s apart in space. A clock traveling at a speed of .6 can be present at both these events. What time interval will such a clock measure between the events? A. 8 s B. 5.8 s C. 5 s D. 4 s E. 2 s F. Other Homework Equations...

Homework Statement I was wondering how one integrates on a open interval. For example let's say I wanted to integrate the function f(x) = x^2 + 2x + 3 on (2,7). Note that it's on the OPEN INTERVAL not closed of all the x values from 2 to 7 not including 2 to 7. I'm not trying to integrate...

Homework Statement Using IVT, show that 3(\cos(\pi x)) - 3x + 1 exists on interval (0,1) Homework Equations None The Attempt at a Solution I think I got the right idea, but on my quiz (this was a question I just had on a quiz) I didn't know if I was finished or not. So when using 0 on the...

Homework Statement Homework Equations d = 2.5 c = pi*d = 7.854 velocity/s ?= c * 2 = 15.7079The Attempt at a Solution Since PR is 1/4 of the circle and the particle moves around the circle 2 times per second, I thought the average velocity would be 1/8th of the velocity that it's traveling...

Homework Statement Twenty-eight children were given a language test with the scores recorded on a scale of 0 to 100. The variance in the test scores serves as a measure of the homogeneity in language skills for children. The sample standard deviation of the test scores was found to be 12...

Homework Statement Ok, so I don't need help with this part, I just got stuck at the following step when attempting to find the interval of convergence: The Attempt at a Solution I got here: -4 < x^2 < 4 So, I need to solve this inequality. But can I? How can I take the square root...

I have been given a data and asked to state the sampling interval Heres what I know The data has a value generated for each month of the year, I have calculated a period of 11 years. Now I know the formula: 2PI/omega = number of samples per period So will Omega = PI/66

Homework Statement Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not. Homework Equations The Attempt at a Solution I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming...

Homework Statement I need a power series with a radius = pi. (So when you do the ratio test on this power series you get pi) Homework Equations The Attempt at a Solution I tried x^n*sin(n) and thought of stuff like that but couldn't come up with a working power series

This is a proof that: There exist interval [A,B] on the real numbers line that is indivisible as a mathematical point is indivisible. ------------------------------ Its a proof by contradiction, starting with premise 1 Proof \aleph L represents the cardinality of all possible...

Homework Statement Hi Please, I need clarification on this queston Show that the equation 0 = x/2 -1/x ,x>0, has a root in the interval [1, 2]. b Obtain the root, using interval bisection two times. Give your answer to two significant figures. Homework Equations Change in...

Homework Statement P(x) is an increasing function and Q(x) is a decreasing function in interval a ≤x≤b, x is positive. P(x) and Q(x) are located in 1st quadrant. Another function γ(x) satisfies m≤γ(x)≤M. Find the value of m and M if: a. γ(x) = P(x) - Q(x) b. γ(x) = P(x) . Q(x) c. γ(x) =...

Homework Statement The voltage at terminal a relative to terminal b of an electric component is given by v(t) = 20\cos(120\pi t) Volts and the current into a is i(t) = -4\sin(120\pi t) amps. Find 1) the total energy that flows into component from time t1 to t2 and 2) in particular find the...

I got a question which has been confused me for a long time. The question is to calculate the 95% confidence interval for a curve. I have already learned how to calculate for a straight line. For example, the cumulative distribution function (CDF) could be expressed as below: Y = 1/2 * {1...

Hi all, I am having a little trouble understanding one of the concepts presented in my calculus class. I do not understand how the endpoints of an open interval can be differentiable. My teacher says that the endpoints of a closed interval can not be differentiable because the limit can not...

Consider the spacetime metric ds^2=-(1+r)dt^2+\frac{dr^2}{(1+r)} + r^2 ( d \theta^2 + \sin^2{\theta} d \phi^2) where \theta, \phi are polar coordinates on the sphere and r \geq 0. Consider an observer whose worldline is r=0. He has two identical clocks, A and B. He keeps clock A with...

Homework Statement Let f be continuous at c and f(c)>0. Prove that there is an open interval (a,b) centered at c such that f(x)>0 for all x that are elements of (a,b) Homework Equations we are supposed to use the sign preserving property?? The Attempt at a Solution I tried...

Can an interval with all positive functions of x be proven?? f(x) has to always be greater that 0. How do you prove this?? f is continuous as c and f(c)>0. prove that there is an open interval (a.b) centered at c such that f(x)>0 for all x that are elements of (a,b)

My biggest qualm with the special theory of relativity and, for that matter, the general theory of relativity is the fact that both assume a little bit too much. My first area of skepticism is that so many cling to these as much as they do to Newton's laws, but there has been no tangible proof...

Hi everyone! I started studying differential equations, but I still didn't understand why the domain of the solutions must be defined in an interval. For example the solution of the following initial value problem: \frac{dy}{dt} + \frac{1}{t}y=0,y(1)=1 is given by y(t)=1/t that has it's...

Homework Statement Define f(x) = |x| - 1, what is f((-2,3])? What is f-1((-2,3])? Homework Equations The Attempt at a Solution [-2,1] is the answer for the first part. I don't understand why though... so you have f((-2,3]) = |(-2,3]| - 1 I don't quite get how to take the...

If I am given a problem that asks of me: What is the largest number of real roots that x^7-x+17=0 can have? Be sure to show why your answer is correct. But it doesn't give an interval to work with, can I just make up my own interval, say [0,3]? Because I know this is continuous and...

Homework Statement I can repeat the proof, but then I won't understand it. How do I prove that an open interval like (1,2) is open?Homework Equations I know it has something to do with neighbourhood with a given epsilon, but I don't really get what a neighbourhood is, I have a maybe rough...

Homework Statement f: [-a,a] >. R is Riemann integrable, prove that ∫[-a, a] ƒ (x) dx = 0 Homework Equations The Attempt at a Solution This only proof below I can think of is rather very calculus-ish.I wonder is there any other proof that is more Real Analysis level for this problem? Thanks...

consider a real function f(x) where x\in[a,b] Why f'(x),\; x\in(a,b)

Homework Statement Suppose [a,b] is a closed interval (on R), and {xn}n>=1 is a sequence such that a) xn belongs to [a,b] b) lim as n--> infinity xn = x exists prove x belongs to [a,b] Homework Equations The Attempt at a Solution Well since any sequence is bounded, then...

Homework Statement Find the radius of convergence and the open interval of convergence for the series \sum^{\infty}_{n=0} \frac{(-1)^{n}\sqrt{(2n)!}}{2^{n}n!}(x-3)^{4n} Homework Equations The Attempt at a Solution See figure attached. I'm just curious if I've done the...

Homework Statement Find the interval of convergence of the series.. Sum from n=1 to infinity of ((-5^n)(x^n))/(n^(1/10)). Find the radius of convergence. Homework Equations Ratio Test -> Lim abs( (An+1)/(An)) as n goes to infinity The Attempt at a Solution I used the ratio...

Homework Statement How much energy is dissipated as heat over 2 minute time interval by a 1.5 k(ohm) resistor which has a constant 20 V potential difference across its leads? Homework Equations deltaV=-Ed The Attempt at a Solution In my notes this is the only equation that seems...

It should perhaps go without saying but I suppose, using the interval halving method for minimizing or maximizing purposes, that you have to choose your points, a and b, well so that you for sure get the global minimum or maximum within those points? Otherwise you'll never find the right point?

Homework Statement the main drawback of rutherford atomic model was that from classical E&M theory ,an electron would radiate energy and thus the radius much decrease. how do i find the time interval over which the electron reaches r=0 when starting r=2.0 x 10^-10 m ??/ Homework Equations...

This isn't a homework question, rather I believe I could use the invariant interval to check if my answers are right sometimes, but we are skipping this part in my class. Anyway I did this problem where there were two trains, one of length L moving to the right with velocity v, and another of...

\sum x^n/4^n*ln(n) I have applied the Ratio Test and I got 1 and I am trying to find the interval of convergence. However, by the Ratio Test, the answer is inconclusive. It does not prove whether it is convergent or divergent. Any ideas? Thanks!

Homework Statement \sum n^(1/2)*x^n where n=1 and goes to infinity. Sorry, I'm new at this. I was kind of hoping to get help finding the interval of convergence. After using the Ratio Test I got for an answer the absolute value of x. I know I have to prove whether or not the...

Homework Statement I have to study the limit of a sequence which is defined as follows. I'm not looking for an answer, just a method of how to do it, or even what this notation means. An = { (\frac{n^{2}}{3n^{3}+1}, \frac{4n^{2}}{n^{2}+1} ] n even An = { (\frac{n^{2}}{6n^{2}-4}...

Hi, I have been asked the following question but I am having trouble with it. Any help would be appreciated. The function f (x) is denfied, on the interval -π <= x < π, as f (x) = -2x and elsewhere by f(x) = f(x + 2π). Carefully sketch the function on the interval [-4π; 4π]. Thanks!

f(t)={sin t, 0<t<pie 0, t>pie} After integrating (sin t)(e^-st) by parts I get -1/s(sin t)e^-st + 1/s Integral[(e^-st (cos t)dt] Looks like I'll be integrating forever. I'm I missing something? Also, is there software you can install to help you type math symbols so...

when we calculate a value, say @95% we get 9.99+- .002 this value is describing a parameter of the true population right? it is not saying 95% of the time we get samples, it will fall in this range correct? We never infer anything about statistics, only parameters of populations right...

Homework Statement Determine all x in [-pi/2, pi/2] at which the graph has horizontal tangents. Homework Equations 1.) f'(x)= 9cos(x)-2sin(x) 2.) f'(x)= -5csc(x) (5cot(x)-csc(x)) The Attempt at a Solution 1.) 9cos(x)=2sin(x) 9/2=sin(x)/cos(x) 9/2=tan(x) and then I'm...

Homework Statement A car moving at a velocity of 20 m/s is behind a truck moving at a constant velocity of 18 m/s. When the car is 50 m behind the front of the truck, the car accelerates uniformly at 1.8 m/s^2. The car continues at the same acceleration until it reaches a velocity of 25 m/s...

Homework Statement Without solving the DE, determine an interval in which a solution to the given initial value problem is certain to exist. Is it certain to be a unique solution? [(pi^2/16) - t^2]y' + y^(1/2)tan(t) = 0 Initial Value: y(3pi/8) = 1Homework Equations dy/dt + p(x)y = q(x)The...

For any two rational numbers q1<q2, card ((q1,q2) cap Q) = card Q, right? How to prove it, if it's true?

Hallo. A question about the relationship between the formulas found using the Lorentz transform and the invariance of the space time interval. Two events A and B occur at the same time and different space locations in system S, where A and B are at rest and at distance x. The system S'...

Hallo I'm new to this (wonderful) forum, and to SR too... I've a general question about the space time interval invariance. Say we have two points A and B, at rest each other, at distance AB. Now A and B simultaneously in their reference frame emit a flash of light. The space time interval...