Interval Definition and 677 Threads

∑((√(x2+1))n22/(3n+n3)) We use the ratio test: ρn = |2(3n+n3)√(x2+1)/(3n+1+(n+1)3)| ρ = |2√(x2+1)| ρ < 1 |2√(x2+1)| < 1 No "x" satisfies this expression, so I conclude the series doesn't converge for any "x". However the answer in the book says the series converges for |x| < √(5)/2. What am...

∑(x2n/(2nn2)) We use the ratio test: ρn = |(x2n2/(2(n+1)2)| ρ = |x2/2| ρ < 1 |x2| < 2 |x| = √(2) We investigate the endpoints: x = 2: ∑(4n/(2nn2) = ∑(2n/n2)) We use the preliminary test: limn→∞ 2n/n2 = ∞ Since the numerator is greater than the denominator. Therefore, x = 2 shouldn't be...

https://www.physicsforums.com/attachments/9527 ok from online computer I got this $\displaystyle\int_0^x e^{-t^2}=\frac{\sqrt{\pi }}{2}\text{erf}\left(t\right)+C$ not sure what erf(t) means

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Proposition 3.7...

image due to macros in overleaf well apparently all we can do is solve this by observation which would be the slope as x moves in the positive direction e appears to be the only interval where the slope is always increasing

Find the radius of convergence and interval of convergence of the series. $$\sum_{n=1}^{\infty}\dfrac{(-1)^n x^n}{\sqrt[3]{n}}$$ (1) $$a_n=\dfrac{(-1)^n x^n}{\sqrt[3]{n}}$$ (2) $$\left|\dfrac{a_{a+1}}{a_n}\right| =\left|\dfrac{(-1)^{n+1} x^{n+1}}{\sqrt[3]{n+1}}...

I have some questions. Let us assume for these questions that I am using the (- + + +) sign convention. Firstly, we know that if you have a parameterized curve ξ(s), then you can find the proper time between two events at points s1 and s2 by using this formula (assuming that the curve is...

212 Let f be the function given by $f(x)=300x-x^3$ On which of the following intervals is the function f increasing (A) $\quad (-\infty,-10]\cup [10,\infty)$ (B) $\quad [-10,10]$ (C) $\quad [0,10]$ only (D) $\quad [0,10\sqrt{3}]$ only (E) $\quad [0,\infty]$ Steps ok this was a little...

I've been going through Bernard Schutz's A First Course in General Relativity, and I'm hung up on his "proof" of the invariance of the interval. At the beginning of section 1.6, he claims that he will prove the invariance of the interval, and after a few lines shows that the universality of the...

OK I just had time to post and hopefully ok but still typos maybe the graph was done in Deimos wanted to try tikx but not sure about the polynomial trying to as many physics homework before classes start on Aug 26 Mahalo

2.3.17 At $t=5\, s$ an object is traveling at $5 \, m/s$. At $t=8\, s$ its velocity is $-1\, m/s$ (a) Find the average acceleration for this interval. $$a_{av}=\frac{v_2-v_1}{t_2-t_1}=\frac{\Delta v}{\Delta t}$$ So $$a_{av}=\frac{-1-5}{8-5}=\frac{-6}{3}=-2 \, m/s$$ book answer $-2\...

Yesterday afternoon I heard (and so did every bird in the district) a very loud, low frequency, double boom which was very vigorous and I suspected all sorts of things but then I thought "double boom!" and (engaging smartarse mode) I informed my wife that it was only a sonic boom. I was later...

Hello, so for a Fourier series in the interval [-L,L] with L=L and T=2L the coefficients are given by $$a_0=\frac{1}{L}\int_{-L}^Lf(t)dt$$ $$a_n=\frac{1}{L}\int_{-L}^Lf(t)\cos{\frac{n\pi t}{L}}dt$$ $$b_n=\frac{1}{L}\int_{-L}^Lf(t)\sin{\frac{n\pi t}{L}}dt$$ But if we have an interval like [0,L]...

I learned that the confidence interval and a two sided hypothesis test (test for difference) agree if both have the same significance level. Is that also true for one sided hypothesis tests? For instance, must a right-tailed Hypothesis test with alpha = 0.05 agree with the 95% confidence level...

With regard to special relativity… Whenever, I come across the spacetime interval, written like this, say, (Δs)2 = (Δt)2 – (Δx)2 – (Δy)2 – (Δz)2 , it is as if it has to be that way. However, it seems to me it is this way by definition and does not have to be so. Sometimes, it seems to be...

For a closed interval ##[a,b]## I have learned that ##U(f,P)-L(f,P)=\frac{(f(b)-f(a))\cdot(b-a)}{N}## where ##N## is the number of subintervals of ##[a,b]## (if ##f## is monotonically decreasing, change the numerator of the fraction to ##f(a)-f(b)##). However, if the interval is half-open, then...

Find Radius and Interval of Convergence for $$\sum_{1}^{\infty}(\frac{x}{sinn})^{n}$$. I don`t have any ideas how to do that :/

I'm doing some exercises about special relativity and one of them asks to find the speed in an arbitrary frame of reference (1) in such a way that it perceives two events at the same time that didn't happen simultaneously in other frame of reference(2). Is it correct to state that if the...

Hey! :o We have the matrix $$A=\begin{pmatrix}2 & 0.4 & -0.1 & 0.3 \\ 0.3 & 3 & -0.1 & 0.2 \\ 0 & 0.7 & 3 & 1 \\ 0.2 & 0.1 & 0 & 4\end{pmatrix}$$ We get the row Gershgorin circles: $$K_1=\{z\in \mathbb{C} : |z-2|\leq 0.8 \} \\ K_2=\{z\in \mathbb{C} : |z-3|\leq 0.6 \} \\ K_3=\{z\in \mathbb{C} ...

Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space? $$ 1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...

I am revisiting the invariant interval spacetime issue , as explained in the book Spacetime Physics by E.F. Taylor and A. Wheeler. The explanation is clear and the invariant interval is correct, based on the data given and this is the whole point I am making, as explained below. In a...

doing #1 ok first I divided thru $$y' + \frac{\ln{t}}{t-3}y=\frac{2t}{t-3}$$ but the $$\exp\int p(t) \, dt$$ step kinda baloated? ok I see the denominator has $t-3$ so presume 3 is one of the interval ends but why 0. ? book answwer is

(a) intial value (b) interval $\displaystyle y^{\prime}= \frac{x(x^2+1)}{4y^3}, \quad y(0)=-\frac{1}{\sqrt{2}}$ rewrite $$\displaystyle\d{y}{x}=\frac{x(x^2+1)}{4y^3}$$ $$\displaystyle y^3\, dy=\frac{x(x^2+1)}{4}\, dx$$ integrate $$\displaystyle\frac{y^4}{4}= \frac{1}{4}\left(\frac{x^4}{4}...

$$\d{r}{\theta}=\frac{r^2}{\theta},\quad r(1)=2$$ from i would deduct that $dr=r^2$ and $d\theta = \theta then$ $$\d{r}{\theta}=\frac{\theta}{r^2} \text{ or } \frac{1}{r^2}dr=\frac{1}{\theta}d\theta$$ intregrate

Please see attached image. When we want to find the area under a curve, we can use the formula ##A = \int_a^b\left|g(x)-f(x)\right|dx## where g(x) is greater than f(x) and both are continuous over the closed interval ##[a,b]## My text, as seen in the picture, described the area under the curve...

Hello I have the exercise below: Consider the function f(x)=1−8x2 on the interval [−5,6]. Find the average or mean slope of the function on this interval, i.e. [f(6)-f(-5)]/[6-(-5)] according to the theorem of laGrange the slope in a continues function which is derivable in an interval...

Homework Statement The series is uniformly convergent on what interval? Homework EquationsThe Attempt at a Solution [/B] Using the quotient test (or radio test), ##|\frac{a_{n+1}}{a_{n}}| \rightarrow |x^2*\sin(\frac{\pi \cdot x}{2})|, n \rightarrow \infty##. However from here I'm stuck...

Let x denote the position of a particle on the number line. From x, it can move to either the point a-a2+ax or to the point x-ax-a+a2 for some fixed 0<a<1. Suppose the particle starts at the origin. Prove that any open interval that is a subset of the interval (a-1,a) contains a point that the...

In the usual relativistic equation, ds2 = (cdt)2 - dx2 - dy 2 -dz2 or dx2 + dy 2 + dz2 - (cdt)2, depending on the convention of your choice, and ds2 is called the spacetime interval between the corresponding events, the square being used to avoid nasty ambiguities and irritating imaginary...

In Special/General Relativity invariance of a space-time interval is just so important. But in Quantum Mechanics, be it non-relativistic or QFT, there seems to be no such parallel. I have always noticed this. I have some ideas about the reason: 1 - it's not part of the theory to have a...

In SR why is the following length-interval invariant (1) $$ 0 = (cdt)^{2}-dx^{2}$$ While, (2) $$ 0 = (cdt)^{2}+dx^{2} $$ is not invariant? The first expressions (1) measures the coordinates of a wavefront propagating away from the observer with the speed och light, and since c is a...

Homework Statement Given: Cn_dot = true event rate = 10 interactions/s p(t')dt' = differential probability of an event Homework Equations p(t')dt' = Cn_dot * exp(-Cn_dot * t') dt' The Attempt at a Solution [/B] I want to sample the time interval using python. But I'm not sure how to go...

Mentor note: Thread moved from the Technical Math section, so there is no template. @yamata1, , in the future, please post homework problems or exercises in the Homework & Coursework sections, not in the Technical Math sections. I have moved your post. Hello, I would like some help with an...

Homework Statement interval of convergence for n=1 to inf (x-2)n / n3n Homework EquationsThe Attempt at a Solution i used the ratio test and solved for x and got that the interval of convergence is from -1 to 5. now i have to test the endpoints to determine which ones will make the series...

A simple random sample of 400 high school football players was taken in order to estimate the mean weight of all high school football players. The sample has a mean of 198 lbs. and a standard deviation 26 lbs. Construct the 99% confidence interval estimate of the mean weight of all high school...

Hey! :o A research institute wants to establish a confidence interval for the quota of working people in a city. Let $\hat{p}_n $ be the estimated quota, based on a sample of size $n$. It is assumed that $n> 30$. How can one determine the length of the confidence interval? Generally this is...

Hey! :o The variable $X$ is normally distributed with unknown expected value $\mu$ and unknown variance $\sigma^2$. I want to determine the confidence interval for $\mu$ for $n=22; \ \overline{X}_n=7.2; \ S'=4; \ 1-\alpha=0.90$. Is $S'$ the standard deviation? (Wondering) In some notes...

Hello! I marked the thread as a basic high school level, because I assume my question is just at that level. ) I am reading some materials on statistics now, and, not having enough background yet, I stumbled upon this sentence: "As an example, 50°C, although five times as large a number as...

Homework Statement Find the general solution of the given differential equation. Give the largest interval I over which the interval is defined.Determine wether there are any transient terms in the general solution11. x\frac {dy}{dx} - y = x^2sin(x) Homework EquationsThe Attempt at a...

Homework Statement For a differential equation I have solution y= (1/3) + ce^(-x^3) where c is a constant The interval of solution is (-inf,inf) that makes sense to me, since e^x never has a value of y that equals zero. Edit: this is the original question: Find the general solution of the...

Can (0,1)\subset\mathbb{R} be divided into an infinite set S of non-empty disjoint subsets? It seams like any pair of points in different subsets of the partitioning must have a finite difference, and so there must be some smallest finite difference overall, d where |S| \leq 1/d. Can someone...

Homework Statement In problems 11-14 verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. Question 13: y'' + y = tanx ; y = -cos(x)ln(sec(x) + tan(x)) Anyways, next problem... In...

What's the interval between photons in stimulated emission? In stimulated emission one photon induces the emission of a second photon whose coherence length, energy, polarisation and direction of travel are all identical to its own. There must be a delay between the two photons, see below, so...

Homework Statement Find the interval of convergence of: ##\sum\frac{n^n}{n!}z^n## Homework EquationsThe Attempt at a Solution I obtained that the radius of convergence is ##1/e## but I am not sure what to do at the end points. For ##z=1/e## I would have ##\sum{n^n}{n!e^n}##. Mod edit: I think...

On the Simpson's Rule wikipedia page they mention in their derivation that the calculation can be simplified if one notices that there is no loss in generality in setting ##a=-1## and ##b=1## for the integral ##\int_{a}^{b}P(x)\cdot dx## as a result of scaling. I'm not entirely sure what...

Homework Statement A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers. Assume the distribution of the measurements to be approximately normal. Construct a 99%...

Homework Statement The following two samples are corrosion values for 20 untreated pipes (Xi) and 20 surface treated pipes (Yi) ∑Xi = 950, ∑Xi2 = 46344 and ∑Yi = 1092, ∑Yi2 = 62136 We want to examine if there is basis to claim that the surface treatment reduce corrosion. a) 1: Find a 95%...

Homework Statement Homework Equations P = I*V energy dissipated = wr = ∫ ( P *dt) ... t is from 0 to .4 seconds vs = 400t^2 = 400 * (.4^2) = 64 V The Attempt at a Solution Using KVL I said Vs ( 64 V) = 100 * i ... I found that I was 64/100 = .64 amps. I then said power is .64 amps ^ 2 *...

Show interval on number line. |x| > 0 Solution: Here, x cannot be 0. If x is 0, |x| > 0 is not a true statement. We know that x can be any number other than 0. <---------------------------------)0(-----------------------------> Correct?

Show interval on number line. |x| < 2 Solution: -2 < x < 2 <-----(---------)------> Left side parentheses = -2 Right side parentheses = 2 Correct?