Interval Definition and 677 Threads

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?!

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...

I got this formula for calculating the distance between spacetime intervals at Wikipedia: ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 Now first I thought the d was supposed to be the Greek delta which my physics teacher uses to indicate a difference of the following variable, instead of just...

1. An example of a discontinuous function on an interval [a,b] that does not assume every value between f(a) and f(b). [edit] My answer to this: Piecewise function f(x)= 1/x, for x greater than and equal to -4 but less than zero (0). And f(x)=1/x for x greater than zero but less than and...

The original series is the sum from n=1 to infinity of (n!*x^n)/(n^n) I used a ratio test to find that the interval of convergence is -e < x < e But now I need to test the endpoints, which means I need to find if the following two series converge: sum from n=1 to infinity of...

Hello there. I understand (to the best of my ability) the Least Upper Bound property and the Nested Interval property, but I don't see how the two are equivalent properties. LUB: If S \subset \mathbb{R} has an upper bound, then S has a LUB Nested Intervals: If I_1 \supset I_2...

suppose there are 2 starships, A and B, moving towards each other wuth a relative velocity of 0.999c. they pass each other at time t=t0. after moving a certian distance (relative), they stop(relative to each other), turn around and again statr moving towards each other with the same velocity, of...

\sum _{n=1} ^{\infty} \frac{x^n}{3^n} = \sum _{n=1} ^{\infty} \frac{x}{3} \left( \frac{x}{3} \right)^{n-1} = \frac{\frac{x}{3}}{1-\frac{x}{3}} = \frac{x}{3-x} \textrm{How can I obtain the interval of convergence of the given series? Thanks.} :smile:

f(x)=x^2-2x+2 Draw the function (I can do that) and deside an interval with the leingth of 3, there by f illustrates on an interval in the leingh of 25/4. (how??) (hope you can read it, I am from Denmark, so i'll try)

Hello, how can I proof this: given: a convex function on an open interval I,which is a subset of R. I have to show that the function can be differentiated on the whole interval. I already proved the following for a<b<c, a,b,c in I: f(b)-f(a))/(b-a)<(f(c)-f(a))/(c-a)<(f(c)-f(b))/(c-b)...

Hello, I am in grade 12 taking math31 which is pretty much a college course. I am not doing that great in it at the moment and I just found this forum with less than 2 months left in the semester. Anyway, there are a few questions I am stuck on. One of them is: (note: all of the '<' are...

Definition of relativity's "interval" Okay I have Kip Thorne's text in front of me that says the following: If (\Delta s)^2 > 0 the events are called spacelike If (\Delta s)^2 = 0 the events are called lightlike If (\Delta s)^2 < 0 the events are called timelike Then I have David W...

In class we were given the following sequence- (0,1 1/2, 3/4, 1 1/8, 15/16, 1 1/32 ...) So it's alternating about zero. We're told then that given any number a>1 it s true to say that the sequence (xn) is eventually confined t [0,a] We now have to prove this... Inworked out the...