Interval Definition and 677 Threads

Homework Statement If a function f is continuous at a point x, then f is bounded on some interval centered at x. That is, \exists M \geq 0 s.t. \forall y, if |x - y| < \delta, then |f(y)| \leq M Homework Equations The Attempt at a Solution Let \varepsilon > 0. Since f is continuous at x...

Homework Statement #5 and #6 of the attached pdf on page 5 (graph on page 4 relates to said problems) Note: The professor did not cover how to do a problem like this, and the book does not have a similar problem, nor any other handouts. This definitely was a unique question. I'm unsure if I...

From Koosis, I pieced together the following algorithm. Is sigma known? Yes? Then calculate the exact confidence interval using a normal distribution to estimate that of the sample means, with mean = the mean of sample means = the mean of the population, \mu_{\overline{x}}=\mu, and...

Maths Quadratic Question Homework Statement Find the interval in which 'm' lies so that the expression \frac{mx^2+3x-4}{-4x^2+3x+m} can take all real values ,where x is real. The Attempt at a Solution i have equated this equation to y y=\frac{mx^2+3x-4}{-4x^2+3x+m}...

http://books.google.com/books?id=qhDFuWbLlgQC&lpg=PP1&pg=PA11#v=onepage&q&f=false" Until he arrives at eq. 1.5 I don't understand the steps, can anyone explain it? thanks

My course notes and textbook express this differently: To construct the confidence interval for diff. between means, Course notes (\bar{x1} - \bar{x2})\pmE Textbook (\bar{x1} - \bar{x2}) - E < \mu1 - \mu2 < (\bar{x1} - \bar{x2}) + E why the difference?

i got this question when i read the proof of stone-weierstrass theorem in baby rudin , page 159 , this inequality seems right when n becomes larger, since 1-nx^2 would be negative and (1-x^2)^n always positive, but i don't know how to proved it rigorously using binomial theorem for all n , or is...

Homework Statement Find the absolute maximum and absolute minimum values of the function (x^3)+(12x^2)-27x+9 on each of the following interval [-10,0] The Attempt at a Solution I got this and its saying its wrong. y'= (3x^2)+(24x)-27 factor: 3(x^2+8x-9) so x=-9 and x=-1 y''=6x+24...

Why is the Time component in the Space Time Interval negative? The space time interval is defined to be: ds^2=dt^2-dx^2-dy^2-dz^2 or depending on the convention used it may also be: ds^2=-dt+dx^2+dy^2+dz^2 The equation is defining distance using the pythagorean theorem. This results...

I am trying to calculate the confidence interval for this problem using my T-84, and it's driving me mad because I'm so close to the correct answer. The problem is Homework Statement The answer to this problem is (22769.83, 30059.41) (This is an example problem.) When I try to duplicate...

Homework Statement simplify: 1. (-∞, -2) ∩ [-2, ∞) 2. (-∞, 5] ∩ [5, ∞) 3. (-∞, 5) U (4, ∞) 4. (-∞, 5) ∩ (3, ∞) Homework Equations The Attempt at a Solution It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these...

Homework Statement If an even degree polynomial of order 2n intersects the x-axis twice, how do I show that the (2n-1) th derivative has a zero in that interval? Homework Equations example: let g(x)=x^3(1-x). Show without computation that g'''(c) =0 for some c in (0, 1). The...

Homework Statement suppose the velocity of a point moving at time t, in seconds along a coordinate line is v(t)= (t+3)/(t^3+t) ft/sec. how far does the point travel during the time interval [1,3]. Homework Equations The Attempt at a Solution im not sure what to do, i used ∫3...

Homework Statement I am not really good with Series so I having a hard time with these problems. http://img835.imageshack.us/img835/858/img1257d.jpg Homework Equations The Attempt at a Solution The part I am stuck is where I highlighted. The first question: The whole thing is squared so I...

Homework Statement In a photographic process, the developing time of prints may be looked upon as a random variable which is normally distributed with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take anywhere from 16.00 to 16.50 seconds...

I've been given the question: In a photographic process, the developing time of prints may be looked upon as a random variable which is normally distributed with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take anywhere from 16.00 to 16.50...

Homework Statement Find the interval of convergence: \sum _{n=1}^{\infty } \frac{(-1)^n (x+2)^n}{3^n\sqrt{n}} Homework Equations The Attempt at a Solution \lim_{n\to \infty } |\frac{(x+2)^{n+1}}{3^{n+1}\sqrt{n+1}}*\frac{3^n\sqrt{n}}{(x+2)^n}| = \lim_{n\to \infty }...

Homework Statement I need help finding the interval of convergence for f(x) = 3/(1-x^4). I think that the summation would be \Sigma 3 (x^4n) from n=0 to infinity, but I'm not sure how to get the interval of convergence. Homework Equations f(x) = 3/(1-x^4) The Attempt at a Solution...

Prediction interval, which brackets!? Hi, this is a quick question for a piece of statistics coursework I am doing. I have made a prediction interval with an upper bound of let's say 30 and lower of 20. I just don't know which brackets to use open or close e.g. (20,30) [20,30] (20,30]...

I know that the spacetime interval is the same in coordinate system moving wrt each other at constant speed. But is it true that the spacetime interval is invariant under rotations? If so can you suggest a proof or post a link to one?

Hi, I am having a major brain fart. I realize that for example, open intervals and R are all topologically equivalent. Similarly, closed, bounded intervals are topologically equivalent And half open intervals and closed unbounded intervals are equivalent But I am having a...

Is the close interval A=[0,1] is compact?

Which of the following has a unique solution on the whole interval (0, pi)? y''+y=0, y(0)=0, y(pi)=0 y''+4y=0, y'(0)=0, y'(pi)=0 (t+1)y''+ty=0, y(1)=1, y'(1)=0 (t-1)y'+2y=0, y(0)=0, y'(0)=1 I'm not sure where to go on this one. I solved the first 2 equations and got: y=c*sin(t) and...

Homework Statement f(x)=x^{0.4} Construct a power series to represent the function and determine the first few coefficients. Then determine the interval of convergence. The Attempt at a Solution Determining the first few coefficients is simple enough. Take the first few...

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

Homework Statement The summation from n=1 to infinity of ((n!)x^(2n))/((2n-1)!) Find the Interval of Convergence of this series. Homework Equations Ratio test The Attempt at a Solution I applied the ratio test, then got x^2 times the limit as n approaches infinity of...

Homework Statement This is the question of mine that I'm having a little confusion about. I know the whole process in which you use the ratio test to determine the radius of convergence and using that you test the end points of the summation to see if they converge at the end points aswell...

Homework Statement For which positive integers k is the following series convergent? (To enter - or , type -INFINITY or INFINITY.) Summation of n=1 to infinity of (n!)^2 / (kn)! Homework Equations ratio test: limit n-->infinity of [((n+1)!)^2/(kn+1)!] / [(n!)^2 / (kn)!] (have the...

So as the title says. How do you calculate the confidence interval that is not on the t-table. For example how do you calculate the confidence interval for 97%? Assume that it is a normal distribution, you are not given σ and that n<30. Is there a formula? Or should i look for a more specific...

Homework Statement Determine the radius of convergence, the interval of convergence, and the sum of the series Summation from k=2 to ∞ of k(x-2)^k+1. Homework Equations ratio test? The Attempt at a Solution possibly take the derrivitive of the power series, then find the sum then integrate...

Homework Statement \Sigma (from index k = 1 until infinity) Within the Sigma is the series : (k! * (x^k)) Homework Equations Ratio Test : lim as k approaches infinity |a(k+1) / ak| The Attempt at a Solution When I apply the ration test to the series and simplify I get lim k...

I know quite well how to do these. However, most of the time, the starting points are just given to me i.e. the a and b values to starting iterating. I was just wondering if you were to find a starting point for x3-x-1 = 0, what would be the best starting point to use the Ralphson-Newton...

I have two questions about the space-time interval question. I'm doing a little research about space time, and about space time intervals, but I'm not sure which equation to take. Some sources say that its s^2 = x^2 - c^2 t^2, other say its s^2 =c^2 t^2 - x^2. So which one do I take? The...

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 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) =...