Interval Definition and 677 Threads

Homework Statement From Spivak: Suppose that ##A_{n}## is, for each natural number ##n##, some finite set of numbers in ##[0,1]##, and that ##A_n## and ##A_m## have no members in common if ##m\neq n##. Define f as follows: ##f(x) = \frac{1}{n}##, if ##x \in A_n## ##f(x) = 0##, if ##x \notin...

Homework Statement A function of a hermitian operator H can be written as f(H)=Σ (H)n with n=0 to n=∞. When is (1-H)-1 defined? Homework Equations (1-x)-1 = Σ(-x)n= 1-x+x2-x3+... The Attempt at a Solution (1-H)-1 converges if each element of H converges in this series, that is (1-hi)-1...

Homework Statement f(x) = (x3 - 1)/(x3 + 1) Homework Equations (d/dx)[f(x)/g(x)] = [f`(x)⋅g(x) - f(x)⋅g`(x)]/[g(x)]2 The Attempt at a Solution f`(x) = [3x2(x3 + 1) - 3x2(x3 - 1)]/[(x3 + 1)]2 f`(x) = 3x2[(x3 + 1) - (x3 - 1)]/[(x3 + 1)]2 f`(x) = 3x2(2)/[(x3 + 1)]2 f`(x) = 6x2/(x3 + 1)2 When I...

I need help determining the interval notation of the inequality below: -9<1/x<=1

Homework Statement Solve the initial value problem and determine at least approximately where the solution is valid (2x-y) + (2y-x)y' = 0 y(1) = 3 Homework EquationsThe Attempt at a Solution I know how to solve it, and I got the correct answer, which was: 7 = x^2 - yx + y^2 and then applying...

Homework Statement This is a problem I have posed for myself. Suppose I have found the probability of something occurring over an angle, so it is the probability of landing at a particular angle over an interval of 2 angles. How would I now find the probability of landing there within a...

Edit Background: The teacher doesn't teach we just do activities and have whole chapters worth of 20 mini assignments due every few days. Yes I did read the book found nothing. 1. Homework Statement The average velocity of a car over a certain time interval is 35 mi/h. If the velocity of the...

I'm struggling to get started with the proof that an open interval D containing x0 exists such that f'(x) ≠ 0 for all x∈D, given f'(x0)≠0. It seems like it should be easy but I've been scratching around for an hour now and have gotten nowhere, could anyone give me some advice to help me along?

Homework Statement...

Hey! :o I have to find the solution of the problem $$u_t(x,t)+u_x(x,t)=\frac{2x}{1+(x-t)^2}u^2(x,t), x \in \mathbb{R}, t>0 \\ u(x,0)=1, x \in \mathbb{R}$$ I found that the solution is $$u(x, t)=\frac{1+x^2-2xt+t^2}{x^2-4xt+2t^2+1}$$ Now we have to look for which values this solution is...

Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way. Consider the following integral (I'm working for finding the volume of a solid of revolution): *\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy Personally I...

Hi all, Say two events happen in the same place according to one observer (1). They are separated in time by 3 years. According to another observer (2) that is moving relative to the first, the events are separated by 5 years. We can calculate, using the invariance of the spacetime interval...

Homework Statement Consider ##\sum\limits_{n=0}^{\infty} \frac{n+1}{(2n)!}(x+1)^{2n+1}##. Find the interval of convergence and sum of the power series. Homework EquationsThe Attempt at a Solution According to the textbook: given the power series ##\sum a_n(x-c)^n## the radius of convergence...

Hello! (Wave) Let $X_1, X_2, \dots, X_n$ a random sample with $E(X_i)=\mu$, $Var(X_i)=\sigma^2 \forall i$. For $0<a<0.5$: show that for any $k \in [0,1]$, the interval $$\left( \overline{X}-z_{k=a} \frac{\sigma}{\sqrt{n}}, \overline{X}+z_{(1-k)=a} \frac{\sigma}{\sqrt{n}}\right)$$ is a...

How do i check for correlation or test for association between a continuous data and nominal data in SPSS? My nominal data is the "type of GPS receiver" and the continuous data is "latency" in seconds.

Ok so what I want to know is, is this valid? If so what does it mean?

Homework Statement Some car tires can develop what is known as "heel and toe" wear if not rotated after a certain mileage. To assess this issue, a consumer group investigated the tire wear on two brands of tire, A and B, say. Fifteen cars were fitted with new brand A tires and thirteen with...

Homework Statement Given critical points (3,-4) and (6,0); interval of increase (3, infinity); interval of decrease (-infinity, 3), find the local maxima/minima and sketch the graph. Homework Equations No relevant equations are given, I believe it's a simple sketch the graph. The Attempt at...

Hello all, I have a homework question that I am almost 100% sure that I solved, so I do not believe that this post should go into the "Homework Questions" section. This thread does not have to do with the answer to that homework question anyways, but rather a curiosity about whether or not this...

I am working on a problem for my Statistics class and I am looking for some clarification and some direction. The questions asks about a study that has been done on the diameter of 50 screws (both digital and vernier scale calipers). The differences in the measured diameters had the following...

I'm a little stuck getting started on this question. $$y''+\tan(x)y=e^x$$ with $$y(0)=1,y'(0)=0$$. I know the existence and uniqueness theorem for an nth order initial value problem How do I apply the theorem?

According to Special Relativity, the same event could have a different time duration and a different space extension for different observers, depending on their frame of reference. Relativity subsequently introduced the the notions of Spacetime as a continuum ( as opposed to the classical...

Some sources have ##ds^{2}=d\tau^{2} ##, and others have ##ds^{2}=-d\tau^{2}##, Does the sign depend on the signature chosen for the metric? Thanks in advance.

Find the explicit solution to $tyy' − 1 = 0$, $y(1) = 4$ and give the interval of validity. $ty \frac{dy}{dt} - 1 = 0$ $y \frac{dy}{dt} - 1 = 0$ ==> $ydy - {1/t} dt = 0$ $ydy = 1/t dt$ $\frac{y^2}{2} = ln(t) + c$$y = \sqrt{2ln(t) + c}$ applying $y(1) = 4$ so the explicit solution is: $C =...

I have read the following from what seems a reliable source: The identification of the spacetime interval with quantum phase applies to null intervals as well, consistent with the fact that the quantum phase of a photon does not advance at all between its emission and absorption. Hence the...

Homework Statement Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function: g(x) = √tan(2x+π) Homework Equations Now to determine the domain, I know that the function under the root cannot be negative. The Attempt at a Solution So after...

Is there an f(x) which is differentiable n times in a closed interval and (n+1) times in an open interval? I think I saw this in a paper related to Taylor's theorem (could be something else though). It didn't make sense to me, how can something be differentiable more in an interval that contains...

I am reading Chapter 1:"Real Numbers" of Charles Chapman Pugh's book "Real Mathematical Analysis. I need help with the proof of Theorem 7 on pages 19-20. Theorem 7 (Chapter 1) reads as follows: In the above proof, Pugh writes: " ... ... The fact that $$a \lt b$$ implies the set B \ A...

This may seem an odd question but it will clear something up for me. Are "The spacetime interval is invariant." and the "The spacetime metric is a tensor." exactly equivalent statements? Does one imply more or less information than the other? Thanks!

Homework Statement A diet pill is given to 9 subjects over six weeks. The average difference in weight (follow up - baseline) is -2 pounds. What would the standard deviation have to be for the 95% T confidence interval to lie entirely below 0? ANSWER: Around 2.6 pounds or less Refer to the...

The question is solve, give transient term and interval of solution for x \frac{dy}{dx}-y = x^2 \sin{x} and the answer key has y=cx-x\cos{x} and (0, \infty). Why wouldn't the interval be (-\infty, \infty)?

HI all, I have the equation, 6x^2-2>9x for which I'm to find the solution set in interval notation. I've rewritten the inequalty as 6X^2-9x-2=0. I tried to factor, but no go. Then I used the quadratic and got 9+/- rad(129)/-18. The answers I get for x are -1.1309 and .1309. The calculator...

How does one prove the following relation? \int_{a}^{b}f(x)dx= \int_{a}^{c}f(x)dx + \int_{c}^{b}f(x)dx Initially, I attempted to do this by writing the definite integral as the limit of a Riemann sum, i.e. \int_{a}^{b}f(x)dx=...

Homework Statement ∞ n=3 ∑ ((-1)n (x+3)3n)/(2nlnn) Find radius of convergence, interval of convergence, values for x which series is: absolutely convergent, conditionally converge or divergence. Homework EquationsThe Attempt at a Solution I applied the Ratio Test and got |(x+3)3| lim...

Hi! I'm a student reading a book given to me by my teacher about relativity and spacetime. It says that the separation between events in spacetime is measured in "intervals," and I can understand that part. What I don't understand is why you subtract the squares of the distance in space instead...

Hello, I am looking for a website that contains information such as the interval between Earth and uranus' closest approach. I can't seem to find exactly what I am looking for, so I was wondering how difficult it would be to calculate this. I am at a loss where to start though... Any pointers...

find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi) would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.

Homework Statement I want to calculate velocity and height at each time interval Time intervals: 1,2,3 (seconds) equilibrium height = 3 meters amplitude = 0.2 angular frequency = 48 rad/s phase shift = 60 Homework Equations y(t) = equiheight + Amplitude*sin(angfre*t +...

Let $I$ be an interval and $A_{n}$ be the set of $k/n$ where $k$ is an integer. Prove that $|I|$ is the limit as $n$ tends to infinity of $\frac{1}{n}|(IA_{n})|$ where $IA_{n}$ denotes intersection. My plan was to split it up into cases for the different type of intervals and come up with...

What is the magnitude of the instantaneous velocity (speed) of a freely falling object 37 s after it is released from a position of rest? Consider the acceleration of gravity to be 10 m/s2 . Answer in units of m/s What is its average speed during this 37 s interval? Answer in units of m/s

Homework Statement Latency Time(years): Number of patients 0: 2 1: 6 2: 9 3: 33 4: 49 5: 66 6: 52 7: 37 8: 18 9: 11 10: 4 (I don't know how to make a proper table with latex... tried \being{tabular}{l r} but this doesn't work) Homework Equations When the variance is...

The question asks Verify that the indicated function $$y=\phi(x)$$ is an explicit solution of the given first order differential equation. Consider $$\phi$$ simply as a function, give its domain. Then by considering $$\phi $$as a solution of the differential equation, give at least one interval...

Hello guys, I would like to calculate the confidence interval of the data in which the data is correct. In otherwords I would like to know how much confidence we have that the data is correct. Could anyone direct me where to start? Thank you.

Before asking a question I would first like to mention the definitions of limit of function and differentiality at x=p 1) Limit of function (f) at x=p Let E be domain of f and p be a limit point of E. Let Y be the range of f. If there exists q∈E such that for all ε>0 there exists δ>0...

Homework Statement Frames S and S' are moving relative to each other along the x and x' axes. They set their clocks to t = t'=0 when their origins coincide. In frame S, Event A occurs at xA = 1 yr and tA = 1 yr, while event B occurs at xB = 2 yr and tB = 0.5 yr. These events occur...

Homework Statement What's the domain of 14/x2-x-6, in interval notation? Homework Equations \underline{14}x2-x-6 The Attempt at a Solution [3, + infinity) [-2,- infinity) Sorry, I can't find the infinity symbol Thx

Show that for every integer $k\ge 2$, the equation $x^k+\dfrac{1}{x^k}=1+x$ has a root in the interval $\left(1, 1+\dfrac{1}{k} \right)$.

Homework Statement 2sin2x + 3sinx - 2>0 and x2 - x - 2 < 0 . x lies in the interval A)∏/6 to 5∏6 B)-1 to 5∏/6 C)-1 to 2 D) ∏/6 to 2 Correct Answer is D, and I get C. Homework Equations The Attempt at a Solution So I factorized the second equation and obtained...

How does one prove the following: \int^{c}_{a} f\left(x\right)dx = \int^{b}_{a} f\left(x\right)dx +\int^{c}_{b} f\left(x\right)dx where f\left(x\right) is continuous in the interval x\in \left[a, b\right], and differentiable on x\in \left(a, b\right). My approach was the following...

Hello. I'm having trouble figuring out from which perspective to measure the proper time interval for Special Relativity. In the textbook, the definition says it's "the time interval between two events measured by an observer who sees the events occur at the same point in space." But in the...