Interval Definition and 677 Threads

Hello everyone! I'm trying to prove that the closure of $A = [-\infty,0)$ is $[-\infty,0]$. So far, I have proved that all points in $[-\infty, 0)$ are limit points of A, then I have proved that $\sup A = 0$, so it is in the closure, so $[-\infty, 0]$ subsets the closure. But how do I know...

I am having trouble understanding how there could be a least upper bound for an open interval. If I have (a,b) and i am looking for the least upper bound X which is the number that is less than or equal to the set of Y such that Y> all the numbers in the interval (a,b) when I think about it I...

Homework Statement On what intervals is the function f(x) = x^4 − 4x^3 both decreasing and concave up? x < 0, 2 < x < 3 x < 3 x < 0, x > 2 x > 0, x < -3 2 < x < 3 Homework Equations The Attempt at a Solution I tried to get the derivative of f(x) to make it greater than 0...

Homework Statement In reference to Galileo's Inclined Plane experiment. 2) What does it mean to say “The ball picked up the same amount of speed in each successive time interval.” Use symbols to write this sentence mathematically. 5) For the ball falling vertically, if we believe that...

Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. 2. Relevant equation ν = L di/dt The Attempt at a Solution I don't understand how the solution gets i = 10.0 A for t = 2 ms as well as to how it gets i = 30 – (10 * 10^3) t) (A) for 2 ms < t < 4...

Homework Statement Calculate the spectral interval (λmax, λmin, and Δλ) in which all the lines of the Lyman, Balmer, and Pashcen series (excluding their continuous parts) of the H-atom are found. Homework Equations Here is where I am confused.. do I use the Balmer's formula for H...

Homework Statement The position of a particle moving along the y-axis has a position given by y = 0.20m + (8.0m/s) t - (10 m/s2) t2. is there any time interval during which the particle is not moving? Homework Equations The Attempt at a Solution I said No but I'm not sure why...

Homework Statement Use the definition of continuity to prove that the function f defined by f(x)=x^(1/2) is continuous at every nonnative number. Homework Equations Continuity in this text is defined as Let I be an interval, let f:I→ℝ, and let c be in I. The function f is continuous...

The Nested interval theorem: If An = [an, bn] is a sequence of closed intervals such that An+1 \subseteq An for all n \in N, then _{n \in n}\bigcapA = ∅. I think of the case where a1=a2=...=an and b1=b2=...=bn for all n, hence every set A(n+1) will be the "subset" of A(n) and the intersection...

I think I said before that the recent glacial era, the late Pleistocene is actually a string of riddles. One of them is the Mystery interval. As the ice core indications in Antarctica suggested a clear warming around 19-18,000 years ago, the ice cores in Greenland did not show anything. On the...

So I know how to find the "Interval of Convergence" for a power series representation of a Function f(x). But I Still don't know what that "Interval of Convergence" does for me other than I can choose a number in it and plug it into the series. For Example[SIZE="4"] e^{x}=\sum^{∞}_{n=0}...

Hello, Let me get right to my problem. I have an experimental distribution and a single-parameter theoretical distribution. I want to find the value for the best fit theoretical distribution that agrees with my experimental data for the bulk of the distributions (the tails of my...

1. Find the radius and the interval of convergence for the series: Ʃ n=2 --> inf : [(-1)nxn]/ [4nln(n)] 2.To find the radius, we use the alternating series test. **an+1/an 3. From the alternating series test I find that the limit as n --> inf = 4. So our radius is 4...

Hello, I am trying to solve the following problem from Sethna's book on statistical mechanics (not homework). On a Highway, the probability of a car passing in some interval dt is \frac{dt}{\tau}; \tau=5min. what is the probability distribution of time intervals \Delta between two...

Hello all, Again I find myself at odds with my online class. Somehow, and with two problems in a row, I am finding the reciprocal answer to what Math Lab is telling me. I would be very appreciative is someone could check my work. Find the limit of convergence, and the radius. \sum...

Since two observers with coinciding origins at t=t'=0 both measures a light wave to be moving at c they will both claim that r^2= (ct)^2 and thus that r^2-(ct)^2 = 0. Thus r'^2 - (ct)^2 = r^2 - (ct)^2 = 0 which is really just stating that 0=0 for events following the spherical wave off...

I took a picture of a simple problem from my Diff Eq book. It is split up into two pictures for better resolution. In summary, ty'+2y=4t^2 (1) Has the solutions, y=t^2+C/t^2 (2) So, equation (1) has infinite solutions of the form of (2). But imposing the initial...

Homework Statement The spacetime interval between the origin in frame S and an event, A, is found to be r = 8 lightseconds. In frame S' moving in Standard orientation with respect to S at speed v = 0.5c event A is measured at a distance r' = 6 lightseconds from the origin. (a) What is...

Could anyone explain how Δs is related to the proper time interval?

In general relativity, we have a gravitational time dilation of: \frac{d\tau}{dt} = \frac{1}{\sqrt{1 - \frac{2GM}{rc^2}}} The term - \frac{2GM}{rc^2} appears to be based on the fact that gravity is attractive. If I understand correctly, if the curvature of space-time leads to attraction, then...

Homework Statement Question Anna is calculating the mean and standard deviation for a set of data for a random variable X. The data is summarised in the table below. x: 10– 20– 30– 40–50 Frequency: 8 20 12 0 (i) For each of the following cases, write...

Hey guys! I am new here, and would like to ask a question that has been on my mind for a very long time. I've searched on the internet to find a solution to this question, but have come up with nothing, so I searched for a physics forum which could possibly put my question to rest. Here it is...

Homework Statement We observe a spaceship moving away from the Earth at a velocity of v = 0.866c. The spaceship emits two light signals, the second one 4 seconds (Delta T') after the first one (measured on board). What is the time interval (Delta T) between the arrival of the two light signals...

If an example was written; h(x) = 1/x and the function h has domain R excluding 0, could somebody please explain how the two open intervals include (- infinity, 0) and (0, infinity)? (Headbang)

Homework Statement (I translated this from french) Some n dice are thrown and the sum of all their face values is 117. Estimate n through a confidence interval of 90%. In other words, of all the possible rolls of n dice that sum up to 117, find a range in which n should be located 90%...

Homework Statement Find the interval of convergence for the given power series. Sum from n=1 to infinty of (x-11)^n / (n(-9)^n) Homework Equations The Attempt at a Solution I used the ratio test and I'm getting 2<x<20, but that doesn't seem to be right. I get abs(1/9*(x-11)) <...

Homework Statement I have found the interval of convergence for the series Ʃ (xn)/(3nn2) to be -3>x>3 and have tested +3 to break down to p series 1/n2 which converges. However I am unsure of the negative endpoint of 3. If I plug it in, the series looks like Ʃ(-3)n/(3nn2). By alternating...

Homework Statement In a primary school, the mean height of the students of primary 1 students is 120cm. Given a sample size of 40, the confidence interval is 117 and 123. Find the confidence interval if the sample size is 30 instead. Homework Equations Standard deviation and confidence level...

This is a 'just for fun' question at the end of my online lecture notes.. My brain is fried from studying for exams, I can't figure it out and it is driving me mad! Anyone care to help me out?

Homework Statement X1,...Xn is a random sample from N(μ, σ^2) Homework Equations Estimator of μ maybe? a1 + a2 = a a1 = a2 = a/2 (x-μ)/(σ/√n)~N(0,1) ((x-μ)/σ)^2~Chi square(1) The Attempt at a Solution I tried to replace μ with its estimator xbar but that gives me 0.

Homework Statement Homework Equations The Attempt at a Solution

Suppose that f is continuous function on the interval [a,b] integral from b to a If(x)I dx =0 if and only if f(x)=0 for all x in [a,b] ıs it true or false ? ı can prove that if f is zero,integral is zero but ı can,'t do that if integral is zero f is zero Regards

Homework Statement Find the area of the surface generated by revolving the curve Homework Equations x = 5(cos3t), y = 5(sin3t), 0 ≤ t ≤ \pi, about the y axis. The Attempt at a Solution x' = -15(cos2t)(sin t) y' = 15(sin2t)(cos t) (I think this forms the top part of an astroid)...

Are there general formulas for Fourier coefficients on an integral [a, a + T], where T is the period. There is a general formula for the coefficients of exponential Fourier series. Are there general formulas for the coefficients of the trigonometric Fourier series that would work on any interval...

Homework Statement A sequence (Xn) is Cauchy if and only if, for every ε>0, there exists an open interval length ε that contains all except for finitely many terms of (Xn). Homework Equations The Cauchy Definition is: A sequence X = (xn) of real numbers is said to be a Cauchy sequence...

Homework Statement Show that if f: [a,b]→Re is increasing and the range of f is a bounded interval then f is continuous. Homework Equations N/A The Attempt at a Solution I have no idea where to start, but I decided to start with a couple of things. Proof: Let f: [a,b]→Re...

Homework Statement Show that if F is continuous on [0,∞) and uniformaly continuous on [a,∞) for some positive constant , then f is uniformaly continuous on [0,∞). Homework Equations The Attempt at a Solution Let I:= [0,∞) and A:=[a,∞) where a ≠0 and I is contained in ℝ and A is...

I THINK this theorem in short words states that if a function is continuous in an interval [a,b] then it has a maximum. But I have a doubt with the demonstration when it supposes an absurd: $$\begin{align} & \text{THEOREM:} \\ & \text{ }f:[a,b]\to \mathbb{R}\text{ continuous} \\ &...

The original problem is as follows: IF E,F are measurable subset of R and m(E),m(F)>0 then the set E+F contains interval. After several hours of thought, I finally arrived at conclusion that If I can show that m((E+c) \bigcap F) is nonzero for some c in R, then done. But such a...

Homework Statement Prove that the closed interval [0,1] is not a homogeneous topology by showing that there's no bijective, open and continuous (bi-continuous) mapping h: [0,1]→[0,1] such that h(1/2)=0.Homework Equations The closed interval is equipped with the usually metric. If the mapping...

Homework Statement The total energy stored in an LC circuit is 2J. The inductance is 10^-2 H and the capacitance is 100 μF. What is the time interval between a maximum current through the inductor and a maximum potential difference in the capacitor?Homework Equations T = 2∏/ω ω = √(1/LC)The...

[b]1. what is the domain of the function k(y)=1/(2y+1)? Express your answer in interval notation [b]2. [b]3. I find that 0.5 is a possibility in this function, but since i have not done functions at school, i do not really know much more of this question.

I decided to make a couple solenoids. Not too many loops on them though as I need higher gauge wire. After getting that I put one in the other and in that a core of metal that had some iron in it. I tried inducing a bit of current in the outer winding by driving DC current through the inner coil...

The following are summary statistics for a data set. Would it be appropriate to use the Student's t- distribution to construct a confidence interval for these data? Explain clearly! Sample size = 10 Mean = 8.905 Median = 6.105 Standard deviation = 9.690 Minimum = 0.512 Maximum = 39.920...

Homework Statement Is the Set X Dense on any interval between (0,1) X= \{ \frac{p}{q} \} where p and q are odd positive integers with p<q The Attempt at a Solution so we know that q is always bigger than p so it will always be less than 1. and since p and q are odd we will not have...

The following are summary statistics for a data set. Would it be appropriate to use the Student's t- distribution to construct a confidence interval for these data? Explain clearly! Sample size = 10 Mean = 8.905 Median = 6.105 Standard deviation = 9.690 Minimum = 0.512 Maximum = 39.920...

Homework Statement The series: \sum^{n=\infty}_{n=0} \frac{(-1)^{n+2}(x^{3}+8)^{n+1}}{n+1} Homework Equations The Attempt at a Solution using the ratio test, I get the following: |x^{3}+8|<1, but I know that the radius of convergence must be in the form: |x-a|<b, where...

Homework Statement here is the series: \sum^{\infty}_{n=0}x(-15(x^{2}))^{n} Homework Equations The Attempt at a Solution I know that -1<-15x^{2}<1 for convergence (because of geometric series properties) but I run into a problem here: -1/15<x^{2}<1/15 You can't...

I've seen a few short proofs that if that some transformation \Lambda preserves the spacetime interval, then \Lambda^\top g \Lambda = g where g is the spacetime metric. They have all relied on an argument using some simple algebra to show that (\Lambda^\top g \Lambda) x \cdot x = g x...

Homework Statement Start with the Bolzano-Weiertrass theorem and use it to construct a proof of the Nested Interval Property. Homework Equations Bolzano-Weiertrass: Every bounded sequence contains a convergent sub-sequence Nested Interval Property: Closed intervals nested inside of each other...