Interval Definition and 677 Threads

[SOLVED] Average Current Through A Coil Over An Interval Homework Statement The problem comes from a homework assignment I have. It has to deal with average current flowing through a wire over an interval. It is stated as follows: A five-turn circular coil of radius 15cm is oriented with its...

[SOLVED] Finding the Max Value of a Function on a closed interval Homework Statement Hi, I'm reposting this because it's a subsection to a larger question I had and I figured more people might be able to help with a new topic name. anyway i have the equation (eq1) C(t) = C + a(e^.5t) +...

Homework Statement A plane lands with a speed of 80.0 m/s and can accelerate with a maximum magnitude of 6.00 m/s^2 as it comes to rest. From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest? b. what is the minimum distance the...

[SOLVED] Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu Homework Statement Sketch the graph of the function on the interval [0, 2pi]. y = cosx - 1/2(cos2x) Homework Equations The Attempt at a Solution so the problems that i have been practicing...

Homework Statement I am given the table \begin{array}{ccccc} samplesite & 1950 & 1975 & Change \\ 1 & 7.30 & 7.70 & 0.40\\ 2 & 6.14 & 6.72 & 0.58 \\ 3 & 6.47 & 6.32 & -0.15 \\4 & 5.87 & 6.38 & 0.51 \\ 5 & 6.06 & 6.34 & 0.28 \\ 6 & 4.71 & 5.78 & 1.07 \\ 7 & 5.45 & 5.59 & 0.14 \\ 8 & 6.17 &...

Graphing a function on a given interval...?? My problem is: Use a graphing calculator to graph the function...? ...over the given interval f(x)= -x^4+3x^3-4x+3 (-2,3). How do you graph something on a specific interval? P.S. I have the Casio fx-9750G PLUS graphing calculator.

Could someone pleases either: a. Justify the notion that the Lorentz interval between two events is independent of the observer, without referring to the Lorentz transformations. b. Derive the Lorentz transformations without resorting to the notion that the space-time interval between two...

Please tell me if it is possible to derive the formula which accounts for the Lorentz contraction from the invariance of the space-time interval. Thanks

Please tell me if the following statement is correct: In cc(dt)^2-(dx)^2=cc(dt')^2-(dx')^2 dx and dx' represent proper length dt and (dt') representing non-proper time intervals.

Don't understand why "an indefinite integral is valid only on a interval" Hi I'm using Stewart's Calculus, in the section of indefinite integral, they say: "Recall from Theorem 4.10.1 that the most general antiderivative on a given interval is obtained by adding a constant to a particular...

For summation from 1 to infinity of x^(n)/[2^(n)*n^(4)] - I get the radius is 2 by ration test, but how do I get the interval, just by pluggin in?

Homework Statement Lets define a function f on an open interval ]0,1[ by setting f(x) = \int_{1/2}^\sqrt{x}} tln\frac{1+t^2}{1-t^2}dt Calculate the first three deriatives f'(x), f''(x) and f'''(x) Homework Equations Product and Quotent rule. The Attempt at a Solution...

Homework Statement the max value of f(x)=x^3(40-x^2) on the closed interval 0<= x <= 40 occurs at x=? The Attempt at a Solution different problem, same story (notes are unclear, and the book only complicates things more). I know the answer is 24, but this will not help me on the final exam...

Homework Statement The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the...

Hi everyone! I'm new here but I really hope you guys can be of some more help then my professor. We have our final exam next week (class ended today!) and the following 2 questions are on our review sheet. However, we NEVER covered this material. I'm terrible at "self taught" math so I'm having...

Homework Statement Find the radius and interval of convergence for the following power series. \sum_{n = 2}^{\infty}\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}x^n The Attempt at a Solution R = \frac {1}{\lim_{n\rightarrow\infty}\sqrt [n]{\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}}}...

The question asks to prove directly that the closed interval is covering compact - U= an open covering of the closed set [a,b] I started by taking C=the set of elements in the interval that finitely many members of U cover. Now I need to somehow use the least upper bound theorem to show...

[SOLVED] A Chebyshev interval with a poisson distribution Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface; the number of these uranium fission tracks on this surface follows a Possion distribution. A particular zircon is of...

The figure below shows a worker poling a boat-a very efficient mode of transportation-across a shallow lake. He pushes parallel to the length of the light pole, exerting on the bottom of the lake a force of 225 N. Assume the pole lies in the vertical plane containing the boat's keel. At one...

I am working on a homework problem, and because it is a homework problem, I will not tell you the specifics or ask for an answer. My question has very little to do with the problem in particular, I just wanted to make that disclaimer. Oh, and the derivation of the Lorentz transformation was NOT...

just a cool fact I thought I'd share with anyone who's interested: The set of real values functions on any interval in R has cardinality at least 2^c. Pf: Consider characteristic functions defined on the interval, (a,b). (Note: a characteristic function is a function that can be defined...

I am working with a linear line with positive slope, the points are given. 1. In interval notation write for which values f(x) > 36 2. At f(x)=36 x=21 3. I think it should look like (-inf,21)

Easy Question but can't seem to make head way on this one! For the Function shown in the link below find and plot f(2 -t/2) http://www.imagedump.com/index.cgi?pick=get&tp=516020

Homework Statement A ball is thrown downward with initial speed of 8m/s from a height of 30m. Homework Equations \After what time interval does the ball strike the ground The Attempt at a Solution acceleration will equal -9.8m/s^2 because it's free fall would i use equation...

1. Find the domain of the function 5x/8x^2+9 in interval notation. 2. 3. I believe the domain is all real numbers, but do not know what that would look like in interval notation. Could someone show me?

Can anyone explain exactly how the diagram in Schutz 'Invariance of the interval' actually shows the rod appears the same length in the two different frames and how in any case that shows the direction of the relative velocity between two frames is irrelevant? I can see that the worldline of...

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...

I am given the four-vector of two events in a reference frame S and I found that they are spacelike. I want to then find the reference frame in which these two events are simultaneous. I am still a bit confused about how this is even possible. There is that equation: gamma * delta t' =...

Find an open interval about a on which the inequality | f(x) - L | < E holds. Then give a value for D > 0 such that for all x satisfying 0 < | x - a | < D the inequality | f(x) - L | < E holds. f(x) = x^2, L = 4, a = -2, E = .5 To solve I setup the inequality Step 1: -.5 < x^2 - 4 <...

When an object is traveling at c the spacetime interval is zero. I can follow the algebra that gets to this conclusion. Is there a conceptual, mentally conceived image, explanation for a spacetime interval of zero ?

Homework Statement Find the radius of converge of: \sum[SIZE="4"]x^{}(n choose k) Homework Equations Radius of converge = 1/limsup|an+1/an|, for power series: anx^n The Attempt at a Solution Tried rewriting (n choose k) as: n!/[k!(n-k)!] but where do I...

Is ther any form by bisection or simiar to obtain a partition for an infinite-dimensional interval (aka functional space)?? i believe you could obtain a partition for every interval 'centered' at a certain function as: X(t), X(t)+\delta (t-t`), X(t)+2\delta (t-t`), X(t)+\delta (t-t`), ...

[Solved]Is a stats question,just need some clarity on it-"total width of less than 2. Homework Statement Hi.The result of a memory test is known to be normally distributed with mean mew and standard deviation 1.0. It's required to have a 95% confidence interval for mew with a total width of...

Hi all, I'm having difficulty proving that all intervals of the real line are connected in the sense that they cannot be decomposed as a disjoint union of two non-empty open subsets. Here is the "proof": Suppose X is an interval and X = (X intersect U) union (X intersect V)...

Hi... I know that this question will be found little bit stupid, but unfortunatly I can't see where I made a mistake. Let's have stick with light sources on both ends. In stick's reference frame the flashes from both sources are simultaneous. In laboratory ref. frame they are not. However...

How do we prove that the spacetime interval is invariant? Also why is it so important?

Homework Statement Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart. What is the time difference between the two events in this second inertial system? Homework Equations...

I hae built a MK111 variable interval timer http://www.maplin.co.uk/Module.aspx?ModuleNo=25224&criteria=TIMER%20KITS&doy=6m1" and intend to use it for a free-flight glider which is a university project! I wish for the timer to power an electric motor for 2sec and then pause for a desired...

i find in the literature in different textbooks the term proper time Thomas A. Moore, Six Ideas that Shaped Physics (McGraw-Hill) 1998 and the term proper time interval Yuan Zhong Zhang, Special Rekativity and its Fundamental Foundations, (World scientific ) I consider that the first is...

Homework Statement Find the absolute max and min of h(x) = cos(2x) - 2sinx in the closed interval [(pie)/2, 2pie] The Attempt at a Solution I got h(x) = cos(2x) - 2sinx h'(x) = -sin(2x)*2 - 2cosx <---chain rule i did :smile: 0=-2sin(2x) - 2cosx 0=[-2sin(2x)/-2] -...

Ok i know it should be because it has the same cardinality as R and R is uncountable. But take for example (0,1). Heres a method I would use to count all its elements: 0.1,...,0.9 0.01,...,0.99 0.001,...,0.999 . . . 0.(n-1 zeros)1,...,0.(n 9's) . . . so count starting from the top...

I need help finding the radius & interval of convergence of the following power series: The sum from n=0 to infinity of... (2-(n)^(1/2)) * (x-1)^(3n) I think the ratio test is supposed to work, but I narrow the limit of the test down to 1/|x-1|^3 < 1, and this doesn't make sense to me. Is...

I just wanted to see if someone could verify my answers: \\sum_{n=0}^\\infty \\frac{(x+7)^n}{sqrt(n)} I get: -8<x<-6 \\sum_{n=1}^\\infty \\frac{(-1)^n*x^2n}{n!} This one I'm not sure of. When I take the limit I get 0. When I solve the inequality I get x. I can't find an...

The question I'm currently working on now is to find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x-2cosx, [-pi, pi] f'(x) = 1+2sinx = 0 From here I've found that -30 degrees(-pi/6) and -150(-5pi/6) degrees are the two intercepts in the equation...

A. Einstein states in The Principle of Relativity, pp 111 - 112: "The modification to which the special theory of relativity has subjected the theory of space and time is indeed far-reaching, but one important point has remained unaffected. For the laws of geometry, even according to the...

Hi, I have a problem that says to solve this equation for the interval 0<theta<2 pie which is one revolution of the unit circle. The equation is: (square root of 2)(cos 2theta) = 1 The cos2theta is a double angle, but I couldn't find any solutions for theta that would = 1 at the end. The...

When a question asks along the lines of : "If a function (g) is decrasing on the interval {x,x)...What would the limg'(x) be (As it approaches infinity)" What are they looking for? and whatequation am I using? I'm not looking for too much info on how to do, but which direction should I go...

Hi I have this series here \sum_{n=1} ^{\infty} \frac{1}{x^2+n^2} I need to show that the Radius of convergens R = \infty and the interval of convergens therefore is (- \infty, \infty) My question is to do this don't I use the ratio-test? Sincerely Yours Hummingbird25

Just what the title says. In the book Spacetime Physics, by Taylor and Wheeler, the time coordinate is measured in metres of light-travel time, but that's just a roundabout way of saying that they are using the second...or am I missing the point. :blushing:

Hi, I was wondering if there was a way to prove the invariance of the space-time interval just from postulating a constant speed of light and an isotropic space-time. Most arguments go "from the Lorentz transformations it can be seen that the interval is invariant." Can we show the...