Interval Definition and 712 Threads

Confidence Interval or the lack of it... It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA, Coffee Pot Attendant. It is a very important office sponsored by the...

Homework Statement If a ball is thrown into the air with a velocity of 40 ft/sec, its height (in feet) after t seconds is given by s(t) = 40t -16t^2. Find the average velocity, vAV (t), of the ball over the time interval (t, 2), for 0 < t < 2. Homework Equations change of x/change of...

Dear all, I'm having confusion about the standard derivation of Schwarzschild's gravitational time dilation. For concreteness I'll follow the explanation of Schutz' "gravity from the ground up", but other texts argue the same. So let me rephrase Schutz's explanation (I surpress factors of c in...

Nearly every analysis reference I come across defines the derivative for functions on an open interval ##f:(a, b) \rightarrow \mathbb{R}##. I understand that, in constructing the definition of ##f## being differentiable on a point ##c##, we of course want it to first be a point it's domain, so...

Homework Statement Both images are 2 consecutive pages of my notes . In this theory , i was told to use z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) . However , in the 2nd image , i was told to replace σ with s ( sample...

I need to find the max/min of a function on an interval. The function is f(x)=x+cos(x) and the interval is <-PI,2pi> There is an attached solution but I do not understand how to arrive at the given solution (see screenshot). I would personally just take the derivative as F'(x)=1-sin(x) However...

Homework Statement Find the Maclaurin series and inverval of convergence for ##f(x) = \log (\cos x)## Homework EquationsThe Attempt at a Solution I used the fact that ##\log (\cos x) = \log (1+ (\cos x - 1))##, and the standard expansions for ##\cos x## and ##\log (x+1)## to get that...

I was trying to show that a closed interval ##[a,b]## and ##\mathbb{R}## cannot be homeomorphic. I would like to know whether this can actually be considered as a proof. It is the following: - The closed interval ##[a,b]## can be written as ##[a,p] \cup [p,b]##, where ##a \leq p \leq...

$\textrm{a. find the power series representation for $g$ centered at 0 by differentiation}\\$ $\textrm{ or Integrating the power series for $f$ perhaps more than once}$ \begin{align*}\displaystyle f(x)&=\frac{1}{1-3x} \\ &=\sum_{k=1}^{\infty} \end{align*} $\textsf{b. Give interval of convergence...

This is not a homework problem so I'm asking it here. I just ran an MCMC and found the best fit parameters for a model of massive gravity. I now need to find the said 68% Confidence Interval interval for those parameters. I have never done anything like this before so I'm clueless where to begin...

I want to plot a function f(x) such that it's domain is from 1 to 10000 but I want the graph to read 1, 10, 100, 1000, 10000 in the x-axis, while the y-axis is normal. ##f(x) = 2\sin^{-1} ( e^{-\frac{60}{x}})##

Homework Statement Consider an observer Bob in S standing close beside the x-axis as Alice, who is holding a clock, approaches him at speed VS'S along the axis. As Alice and her clock move from position A to B, Alice’s clock will measure a (proper) time interval ∆t0, but as measured by Bob’s...

if in 100 years of records you have had floods in five of those years is the flood frequency 5 per 100 years ? and would the flood return interval be every 20 years?

Homework Statement find domain f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ## Homework EquationsThe Attempt at a Solution [/B] Well, one sees that x ≠5 and then we further investigate the dividend portion where the under-the-root expression ≥ 0 We can graph the parabola, and find the zeroes. Then...

This question has a little bit of physics in it, but it's mostly maths. If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I...

If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I assumed the spring force, which is a function of its elongation x (F =...

Homework Statement Starting from rest, a wheel has constant α = 3.0 rad/s2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval? ω0 = 0 α = 3.0 rad/s2 θf = 120 rad Homework Equations Δθ = ω0⋅t + ½αt2 The Attempt at a Solution 120...

I have a question regarding when to go for standard deviation σ or confidence interval ci. I am not sure of how to interpret ci. It seems to give me an option to choose the level of confidence, but I don't see why the the ci is divided by the root of the number of samples. Any pointers would be...

Hello, please note that the following is only about special relativity, not general. Of course, if there are any things to point out that fall in general relativity, feel free to do so, but I don't know GR, so I won't understand arguments based in GR. I also am not great with a geometry-based...

I am reading Larson's Calculus textbook and come across this paragraph about vector-valued function: The parametrization of the curve represented by the vector-valued function $$\textbf{r}(t) = f(t)\textbf{i} + g(t)\textbf{j} + h(t)k$$ is smooth on an open interval $I$ when $f'$, $g'$ and...

It seems that, in general, mathematicians prefer the (-,+,+,+) signature for the Minkowski spacetime metric while most physicists prefer the (+,-,-,-) signature. Is there any evidence that Nature actually prefers one over the other? As usual, thanks in advance.

Hey! :o We have a 90%-confidence interval. I want to check if the following statements are correct. 1. If double the sample, the possibility that the value that we are looking for is out of the confidence interval is smaller. 2. The bigger the standard error, the smaller the confidence...

Homework Statement let fx, gx be continuous in [a,b] and differentiable in (a,b). at the end of the interval f(a) >= g(a). and f'(x) >g'(x) for a<x<b. proof f(x) > g(x) for a<x<=b Attempt: There is a statement says that if the f'x = g'x for x in [a,b] , then there exists k such that f'x -...

Homework Statement I am trying to solve a system of 2 ordinary differential equations using matlab. However, I am not able to get numerical solutions from the code despite having keyed in all possible solutions. Homework Equations The equations I am given are: dx/dt=A(x/t)+By...

Homework Statement The question was to find the interval of convergence for a series. Homework Equations an+1/an The Attempt at a Solution

Problem: y'=((x-1)/(x^2))*(y^2) , y(1)=1 . Find solutions satisfying the initial condition, and determine the intervals where they exist and where they are unique. Attempt at solution: Let f(x,y)=((x-1)/(x^2))*(y^2), which is continuous near any (x0,y0) provided x0≠0 so a solution with y(x0)=y0...

When one reduces the intensity of let's say, an incandescent bulb (by varying the resistance, as seen in many homes), which decreases more, the photon frequency (not related to wavelength, but the time interval between photon emissions) or the areal density of the photons? To what extent does...

Hi, I drew the graph 1. Minumum value of the function = -7 can you help me to write the values for which the function is increasing interval -6<y<0 also can you help me to find the roots of the equation and obtain \sqrt{7} to the nearest decimal place. Help me to proceed Many Thanks...

When we talk about differentiability on a Set X, the set has to be open. And if a set X is open there exists epsilon> 0 where epsilon is in R. Then if x is in X, y=x+ or - epsilon and y is also in X But this contradicts to what i was taught in high school; end points are excluded in the open...

So I have $$\sum_{n = 2}^{\infty} \frac{1}{nln(n)}$$ I'm trying to apply the limit comparison test, so I can compare it to $b_n$ or $\frac{1}{n}$ and I can let $a_n = \frac{1}{nln(n)}$ Then I get $$\lim_{{n}\to{\infty}} \frac{n}{nln(n)}$$ Or $$\lim_{{n}\to{\infty}} \frac{1}{ln(n)}$$ Which is...

I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...

This is the word problem I am faced with... I have provided my answer. Please give input if I am right or wrong. It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA...

Let f(x) = (1+x)-4 Find the Taylor Series of f centered at x=1 and its interval of convergence. \sum_{n=0}^\infty f^n(c)\frac{(x-c)^n}{n!} is general Taylor series form My attempt I found the first 4 derivatives of f(x) and their values at fn(1). Yet from here I do not know how to find the...

Why is it that in SR we always seem to jump to the Lorenz equations when there is a simpler way. This is the concept of an interval. The interval is defined as the square root of ( T squared minus X squared) . In Special relativity the time and distance are different for different...

can we use frequency and time period terms for digital signals or we have to use bit rate and bit interval terms for digital signal. in simple words,

Homework Statement 1-9: Assume the train is 1.0km long as measured by the observer at C' and is moving at 150km/h. What time interval between the arrival of the wave fronts at C' is measured by the observer at C in S? [/B]Homework EquationsThe Attempt at a Solution The solution from the...

Hello! Suppose a quartic polynomial with real roots where all its roots lie in the interval $$x \in \left[\frac{5}{8}a-\frac{3}{8}\sqrt{15a^2-16b}, \frac{5}{8}a+\frac{3}{8}\sqrt{15a^2-16b}\right]$$ where $a \in \mathbb{R}$ and $b<(15/16)a^2$. Is there a way to check that at least one of those...

Homework Statement At time t, the position of a body moving along the s-axis is s= t^3 -12t^2 + 36t m(meters) Find the total distance traveled by the body from t = 0 to t = 3. Homework Equations Derivatives The Attempt at a Solution I got the derivative which is 3t^2 - 24t + 36(meters) I...

Homework Statement dy/dx = (9x²)/(9y²-11) , y(1)=0 Homework EquationsThe Attempt at a Solution I've found the particular solution: 3y³-11y = 3x³-3 The solution is defined for -⅓√11<y<⅓√11, What about the x values? Plugging the y values into the equation doesn't work of course..

Hello Physicsforum Homework Statement I have a problem proving this: Given C(x)=[0, 3/x] for all x\in\chi, with \chi=\Omega being the sample space and P_q=Geom(q) being the geometric distribution. I have to show that C(x) is a confidence Interval for q but I don't know how to get started...

Essentially, I have a function of two variables f(x, y), and I want to find the total value (sum) of that function for all values of (x, y) over an interval. How would I do that? The closest thing I can think of is the mean value theorem for integrals, but I want the total value, not the average...

Homework Statement The interval of convergence of the Taylor series expansion of 1/x^2, knowing that the interval of convergence of the Taylor series of 1/x centered at 1 is (0,2) Homework Equations If I is the interval of convergence of the expansion of f(x) , and one substitutes a finite...

Please help me find my mistake - "find the Sine F/series of f(x)=x over the half-interval (0,L)" I get $ b_n=\frac 2L \int_{0}^{L}x Sin \frac{2n\pi x}{L} \,dx $ $ = \frac 2L \left[ x(-Cos \frac{2n\pi x}{L}. \frac{L}{2n\pi x}\right] + \frac {1}{n\pi} \int_{0}^{L} Cos \frac{2n\pi x}{L} \,dx$...

Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x^2 − 5x + 2 and y = −x^2 + 5x − 6 for x in [0, 4]

I run an algorithm that outputs a normally distributed random number with unknown mean and variance. I need to know the mean of those numbers. To do that, i repeatedly run that algorithm to obtain many numbers, then I calculate the mean and the confidence interval for the mean. Over the last...

I have a question I've been working on and I've noticed that my solution differs from the textbook solution. I would have considered it a mistake, but the next 4 questions are similar with the same solution "mistake"? Aside from not converting the % to 0.885, I am wondering about part b. It...

Homework Statement Find the interval of convergence of the power series ∑(x-2)n / 3n Homework Equations ρn = |an+1| / |an| The Attempt at a Solution I got that ρn = | (x-2) / 3 |. I set my ρn ≤ 1, since this is when the series would be convergent. Manipulating that expression, I got that the...

Hi hi, So I worked on this problem and I know I probably made a mistake somewhere towards the end so I was hoping one of you would catch it for me. Thank you! Pasteboard — Uploaded Image Pasteboard — Uploaded Image

Homework Statement My (practise) coursework is to test the equation 'V = Vo e-t/RC' and choose values of R and C so that the voltage across the capacitor falls to half in 15 seconds. I decided it would be too difficult and inaccurate to record the voltage across the capacitor every 5 seconds...

Homework Statement Let f: [0,2]\to\mathbb{R} be continuous and f(0) = f(2). Show that there exist x,y\in [0,2] with the following property: (*)\ y-x = 1 and f(x) = f(y)\ (*) Homework Equations Bolzano-Cauchy theorem: If a function f is continuous in some interval [a,b] and f(a) <0, f(b) > 0 (or...