Uniform Definition and 1000 Threads

I'm working on a problem for my analysis class. Here it is: Let f be differentiable on an open subset S of R. Suppose there exists M > 0 such that for all x in S, |f'(x)| ≤ M, i.e. the derivative is bounded. Show that f is uniformly continuous on S. I'm not too sure that this question is...

I am given the moment of inertia of the system ( a fan) and the question asks for me to find the angular acceleration "after the fan is turned on, it takes t = 3.6 s and a total of 12 revolutions to accelerate up to its full speed" ? How I went about solving is that.. I simply converted the rev...

Probably is a silly question, but how could I prove that the function (expressed in polar coordinates) \left(\rho^4\cos^2{\theta} + \sin^3{\theta}\right)^{\frac{1}{3}} - \sin{\theta} converges to 0 as rho->0 uniformely in theta (if it is true, of course)?

Two masses connected by a string uniform circular motion. HELP! :) Homework Statement A puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless, horizontal table. The other end of the string passes through a small hole in the center of the table...

Arnold is jogging west at 5 kph along a trail. Ivan is jogging east on the same trail at 3.75 kph.If they are 0.5 km apart, how long will it be until they meet? Help Pleaseeeeeeeeeeee! I need it now. Thank you!

Why some functions that are continuous on each closed interval of real line fails to be uniformly continuous on real line. For example x2. Give conceptual reasons.

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Homework Statement A function f:(a,b)\to R is said to be uniformly differentiable iff f is differentiable on (a,b) and for each \epsilon > 0, there is a \delta > 0 such that 0 < |x - y| < \delta and x,y \in (a,b) imply that \left|\frac{f(x) - f(y)}{x - y}-f'(x)\right| < \epsilon. Prove that...

Homework Statement Find the potential and force on a mass m outside and inside the Earth in terms of g, the acceleration due to gravity, assuming Earth has uniform density and radius R.Homework Equations For a mass m, the potential energy of it in the gravitational field of a spherical shell of...

Hey all, been struggling through this question all afternoon, was wondering if someone could shine some light on the subject please? QUESTION: If a uniform lateral pressure of 80MN/m (2), is applied to the four sides of the bar, in addition to the axial load, find the contraction on the...

This isn't so much of a homework problem as a general question that will help me with my homework. I am supposed to prove that a given function is uniformly continuous on an open interval (a,b). Since for any continuous function on a closed interval is uniformly continuous, I am curious...

Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M

I am given f_n(x)=\frac{nx}{nx+1} defined on [0,\infty) and I have that the function converges pointwise to 0 \ \mbox{if x=0 and} 1\ \mbox{otherwise} Is the function uniform convergent on [0,1] ? No. If we take x=1/n then Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5...

Homework Statement Find the minimum number required (value of n) for the average deviation of the Fourier Series to fall below 2% Homework Equations Use the Uniform Convergence of Fourier Series. Where Sm is the partial sum of the Fourier Series. C is constant. Here C is ∏^2 So...

Homework Statement A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of...

Homework Statement A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum? Homework Equations The Attempt at a Solution

Please look at the picture... It is of a blue object in four locations that is swung around with a rope ( red line ) in a circle with constant velocity... I wanted to know if my diagrams are correct for each separate location... and I was hoping someone could check my work below to tell me...

Homework Statement A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.01 m/s in a horizontal circle, as illustrated in the figure. If the angle the string makes with the vertical is 38°, and the tension of the string...

The problem statement Let f:[a,b]→\mathbb{R} be differentiable and assume that f(a)=0 and \left|f'(x)\right|\leq A\left|f(x)\right|, x\in [a,b]. Show that f(x)=0,x\in [a,b]. The attempt at a solution It was hinted at that the solution was partly as follows. Let a \leq x_0 \leq b. For all x\in...

Homework Statement I'm being given problems regarding the center of mass of a uniformly dense object, and I am told by the textbook to use: \frac{1}{V}\int x dV I have no idea what to do with that. I'm pretty sure I won't be learning anything about multiple variable integrals for two...

1. At a distance of 25km from the eye of a hurricane, the wind is moving at 180km/h in a circle. What is the magnitude of the centripetal acceleration, in meters per second squared, of the particles that make up the wind? Homework Equations Ac=V^2/r = 4∏^2r/T^2 = 4∏^2rf^2 The Attempt...

Homework Statement A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle. (a) What is the speed of its center of mass when...

Homework Statement This is supposed to be a simple problem that shows that light bends or gets pulled in a gravitational field. A light pulse emitted in the positive x direction travels 10 s in a uniform gravitational field of 100 m/s^2. the gravitational field points in the negative y...

Homework Statement Question: A 3.45 kg object is attached to a vertical rod by two strings as in Figure P6.11. The object rotates in a horizontal circle at constant speed 5.65 m/s. What are the tensions of the two strings, individually? Variables: m = 3.45kg length of both strings...

b]1. Homework Statement [/b] An object was displaced 19.6 m east while uniformly accelerating from rest. If the average velocity of the object was 5.00 m/s east, what was the rate of acceleration? Homework Equations The Attempt at a Solution So my Vo=0 Vf= 5.00m/s east x=19.6m...

Homework Statement A uniform ladder of length L and mass M has one end on a smooth horizontal floor and teh other end against a smooth vertical wall. The ladder is initially at rest in a vertical plane perpendicular to the wall and makes an angle \theta0 with the horizontal. (a) Write down the...

Homework Statement What is the acceleration (in m/s^2) of a 10 kg mass moving with speed 2 m/s in uniform circular motion about a circle of radius 2m? Homework Equations F=ma a=v^2/r in uniform circular motion The Attempt at a Solution Seems simple enough. To find the...

suppose we have many dots on a unit n-sphere i suspect that they satisfy the uniform distribution but how to verify this?

Homework Statement A child pushes his friend in a wagon along a horizontal road and then let's go. The wagon rolls for 10.0 seconds before stopping. It travels a distance of 20.0cm during the last 1.00s of its motion. Assuming uniform acceleration, (a) How fast was the wagon traveling at the...

Homework Statement A car accelerates uniformly from rest to a speed of 23.2 km/h in 5.4s. Find the distance it travels during this time. Answer in units of m. Homework Equations \Deltax = 1/2(vi + vf)t vf = vi + at vf2 = vi2 + 1/2 at2 The Attempt at a Solution I have used...

Homework Statement A small 10.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 60.0g and is 90cm in length...

I am in an error analysis class and our homework has asked us this (we will be writing a computer program to do this): "Create a sample with 396 draws from a Poisson distribution with N=1000 and 4 draws from the uniform distribution between 0 and 105. This sample represents data from a CCD...

Homework Statement Hello new user here. I'm utterly confused about uniform acceleration as my book does a very poor job (in my opinion) of explaining it. Could somebody please help me with this problem? A spaceship far from any star or planet experiences uniform acceleration from 65.0m/s to...

Homework Statement car travels in a flat circle of radius r. at certain point instantaeous velocity is 24 m/s west and the total acceleration is 2.5 m/s2 53 degrees north of west. find radial and tangential acceleration. and periodHomework Equations ar= 2.5cos37 at=2.5sin37 r=24 x 24/ar T=...

Hi, Is there any way to analytically calculate the perturbation of a uniform electrostatic field by a dielectric cube. I know a solution exists for dielectric spheres but I haven't been able to come across the solution, when dealing with a cube. Ohh.. and I'm assuming the simplest case...

X is a uniformly distributed random variable on a [-1, 1] range. (i.e. X is U(-1, 1)) Find the distribution of e^2X: I feel like it has something to do with the uniform's relation to exponential function, but i get stuck. I begin by using inverse transform: Fy(y) = Fx[ln(y)/2] fy(y)...

Homework Statement This is more of a general question but it is part of my physics course so i decided to post here, I am sure many of you have done this lab but what it is is a cart with tickertape attached to it going down a ramp, once we plot a d-t graph there are lots of application...

i need to prove that \frac{1}{\sqrt{x}} is not uniformly continues in (0,1) for epsilon=0.5 |\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}|=|]\frac{\sqrt{y}-\sqrt{x}}{\sqrt{xy}}\frac{\sqrt{y}+\sqrt{x}}{\sqrt {y}+\sqrt{x}}|=|\frac{y-x}{(\sqrt{y}-\sqrt{x})\sqrt{xy}}|...

Homework Statement Electric dipole makes small angle with uniform electric field. Find the frequency of the oscillation using dipole moment p, moment of inertia I, and field magnitude E. Homework Equations Torque=I*(angular acceleration)=I*(theta)'' Torque=p*E*sin(theta) The...

I'm not sure this is the right thread to post my problem : I'm trying to define a uniform distribution on the toroidal surface associated to a dipolar magnetic field (or electric). More specifically, the surface (in 3D euclidian space) is parametrised as this, using the usual polar...

Homework Statement An electron with speed 2.0E7 m/s is traveling parallel to a uniform electric field of magnitude 1.18E4 N/C. How far will the electron travel before it stops? How much time will elapse before it returns to its starting point q = 1.60E-19 C mass of electron = 9.11E-31...

How is tangential accleration zero in uniform circular motion?? Homework Statement the magnitude of tangential velocity is same but the directions are different..so how can the tangential acceleration be zero?? Homework Equations The Attempt at a Solution

Homework Statement http://i54.tinypic.com/2uztu6d.jpg Homework Equations I don't know how to use LaTeX, sorry... mass = L times integral of density, where the endpoints are the bounds of the region. However, in this case...it seems to me that things are reserved... The Attempt at...

Is it true that a cauchy sequence of continuous functions defined on the whole real line converges uniformly to a continuous function? I thought this was only true for functions defined on a compact subset of the real line. Am I wrong?

In a uniform electrical field, why does the field strength remain constant? For a field where two metal plates, one negatively charged the other positively charged, why will E, electric field strength, always remain constant? If we assume the distance between two plates A & B, where A has a...

A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. The sensor measures the magnitude of the normal force that the seat exerts on a rider. The loop-the-loop ride is in the vertical plane and its radius is 21 m...

Lewis is a trapeze artist. He is hanging upside down on a swing bar; he is holding on to the swing bar with his knees. Lewis is holding his partner Amanda below him, who weighs 475 Newtons. Assume that Amanda moves on a circle that has a radius of 6.50 meters. At a swinging speed of 4.00 m/s...

The Earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the Earth is a sphere with a radius of 6.38 x 106 m, determine the speed and centripetal acceleration of a person situated at a latitude of...

Homework Statement Revered members, please see my attachment (1) In this diagram, PQRS is a rectangular current loop and I is the current and its direction is shown in red arrow . B is the magnetic field and it acts from left to right and n is the normal drawn to the plane of the loop...

Hello! I have a problem which is solvable using simpler methods, but I'm trying to use it as a bridge to understanding how to do these problems in a more rigorous setting. Homework Statement A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/hr to 50 km/hr in the...