Interval Definition and 677 Threads

Homework Statement The voltage at terminal a relative to terminal b of an electric component is given by v(t) = 20\cos(120\pi t) Volts and the current into a is i(t) = -4\sin(120\pi t) amps. Find 1) the total energy that flows into component from time t1 to t2 and 2) in particular find the...

I got a question which has been confused me for a long time. The question is to calculate the 95% confidence interval for a curve. I have already learned how to calculate for a straight line. For example, the cumulative distribution function (CDF) could be expressed as below: Y = 1/2 * {1...

Hi all, I am having a little trouble understanding one of the concepts presented in my calculus class. I do not understand how the endpoints of an open interval can be differentiable. My teacher says that the endpoints of a closed interval can not be differentiable because the limit can not...

Consider the spacetime metric ds^2=-(1+r)dt^2+\frac{dr^2}{(1+r)} + r^2 ( d \theta^2 + \sin^2{\theta} d \phi^2) where \theta, \phi are polar coordinates on the sphere and r \geq 0. Consider an observer whose worldline is r=0. He has two identical clocks, A and B. He keeps clock A with...

Homework Statement Let f be continuous at c and f(c)>0. Prove that there is an open interval (a,b) centered at c such that f(x)>0 for all x that are elements of (a,b) Homework Equations we are supposed to use the sign preserving property?? The Attempt at a Solution I tried...

Can an interval with all positive functions of x be proven?? f(x) has to always be greater that 0. How do you prove this?? f is continuous as c and f(c)>0. prove that there is an open interval (a.b) centered at c such that f(x)>0 for all x that are elements of (a,b)

My biggest qualm with the special theory of relativity and, for that matter, the general theory of relativity is the fact that both assume a little bit too much. My first area of skepticism is that so many cling to these as much as they do to Newton's laws, but there has been no tangible proof...

Hi everyone! I started studying differential equations, but I still didn't understand why the domain of the solutions must be defined in an interval. For example the solution of the following initial value problem: \frac{dy}{dt} + \frac{1}{t}y=0,y(1)=1 is given by y(t)=1/t that has it's...

Homework Statement Define f(x) = |x| - 1, what is f((-2,3])? What is f-1((-2,3])? Homework Equations The Attempt at a Solution [-2,1] is the answer for the first part. I don't understand why though... so you have f((-2,3]) = |(-2,3]| - 1 I don't quite get how to take the...

If I am given a problem that asks of me: What is the largest number of real roots that x^7-x+17=0 can have? Be sure to show why your answer is correct. But it doesn't give an interval to work with, can I just make up my own interval, say [0,3]? Because I know this is continuous and...

Homework Statement I can repeat the proof, but then I won't understand it. How do I prove that an open interval like (1,2) is open?Homework Equations I know it has something to do with neighbourhood with a given epsilon, but I don't really get what a neighbourhood is, I have a maybe rough...

Homework Statement f: [-a,a] >. R is Riemann integrable, prove that ∫[-a, a] ƒ (x) dx = 0 Homework Equations The Attempt at a Solution This only proof below I can think of is rather very calculus-ish.I wonder is there any other proof that is more Real Analysis level for this problem? Thanks...

consider a real function f(x) where x\in[a,b] Why f'(x),\; x\in(a,b)

Homework Statement Suppose [a,b] is a closed interval (on R), and {xn}n>=1 is a sequence such that a) xn belongs to [a,b] b) lim as n--> infinity xn = x exists prove x belongs to [a,b] Homework Equations The Attempt at a Solution Well since any sequence is bounded, then...

Homework Statement Find the radius of convergence and the open interval of convergence for the series \sum^{\infty}_{n=0} \frac{(-1)^{n}\sqrt{(2n)!}}{2^{n}n!}(x-3)^{4n} Homework Equations The Attempt at a Solution See figure attached. I'm just curious if I've done the...

Homework Statement Find the interval of convergence of the series.. Sum from n=1 to infinity of ((-5^n)(x^n))/(n^(1/10)). Find the radius of convergence. Homework Equations Ratio Test -> Lim abs( (An+1)/(An)) as n goes to infinity The Attempt at a Solution I used the ratio...

Homework Statement How much energy is dissipated as heat over 2 minute time interval by a 1.5 k(ohm) resistor which has a constant 20 V potential difference across its leads? Homework Equations deltaV=-Ed The Attempt at a Solution In my notes this is the only equation that seems...

It should perhaps go without saying but I suppose, using the interval halving method for minimizing or maximizing purposes, that you have to choose your points, a and b, well so that you for sure get the global minimum or maximum within those points? Otherwise you'll never find the right point?

\sum x^n/4^n*ln(n) I have applied the Ratio Test and I got 1 and I am trying to find the interval of convergence. However, by the Ratio Test, the answer is inconclusive. It does not prove whether it is convergent or divergent. Any ideas? Thanks!

Homework Statement \sum n^(1/2)*x^n where n=1 and goes to infinity. Sorry, I'm new at this. I was kind of hoping to get help finding the interval of convergence. After using the Ratio Test I got for an answer the absolute value of x. I know I have to prove whether or not the...

Homework Statement I have to study the limit of a sequence which is defined as follows. I'm not looking for an answer, just a method of how to do it, or even what this notation means. An = { (\frac{n^{2}}{3n^{3}+1}, \frac{4n^{2}}{n^{2}+1} ] n even An = { (\frac{n^{2}}{6n^{2}-4}...

Hi, I have been asked the following question but I am having trouble with it. Any help would be appreciated. The function f (x) is denfied, on the interval -π <= x < π, as f (x) = -2x and elsewhere by f(x) = f(x + 2π). Carefully sketch the function on the interval [-4π; 4π]. Thanks!

f(t)={sin t, 0<t<pie 0, t>pie} After integrating (sin t)(e^-st) by parts I get -1/s(sin t)e^-st + 1/s Integral[(e^-st (cos t)dt] Looks like I'll be integrating forever. I'm I missing something? Also, is there software you can install to help you type math symbols so...

when we calculate a value, say @95% we get 9.99+- .002 this value is describing a parameter of the true population right? it is not saying 95% of the time we get samples, it will fall in this range correct? We never infer anything about statistics, only parameters of populations right...

Homework Statement Determine all x in [-pi/2, pi/2] at which the graph has horizontal tangents. Homework Equations 1.) f'(x)= 9cos(x)-2sin(x) 2.) f'(x)= -5csc(x) (5cot(x)-csc(x)) The Attempt at a Solution 1.) 9cos(x)=2sin(x) 9/2=sin(x)/cos(x) 9/2=tan(x) and then I'm...

Homework Statement A car moving at a velocity of 20 m/s is behind a truck moving at a constant velocity of 18 m/s. When the car is 50 m behind the front of the truck, the car accelerates uniformly at 1.8 m/s^2. The car continues at the same acceleration until it reaches a velocity of 25 m/s...

Homework Statement Without solving the DE, determine an interval in which a solution to the given initial value problem is certain to exist. Is it certain to be a unique solution? [(pi^2/16) - t^2]y' + y^(1/2)tan(t) = 0 Initial Value: y(3pi/8) = 1Homework Equations dy/dt + p(x)y = q(x)The...

For any two rational numbers q1<q2, card ((q1,q2) cap Q) = card Q, right? How to prove it, if it's true?

Hallo. A question about the relationship between the formulas found using the Lorentz transform and the invariance of the space time interval. Two events A and B occur at the same time and different space locations in system S, where A and B are at rest and at distance x. The system S'...

Hallo I'm new to this (wonderful) forum, and to SR too... I've a general question about the space time interval invariance. Say we have two points A and B, at rest each other, at distance AB. Now A and B simultaneously in their reference frame emit a flash of light. The space time interval...

Problem (in my words): So, in music, the interval of an octave between two tones corresponds to doubling the frequency of the oscillation. In early Greek music, the interval of a fifth corresponded to multiplying the frequency by 3/2. With this definition of a fifth, prove that non of the...

Is the interval I of an autonomous diff closed? Homework Statement Given this autonomous diff.eqn Where we have an open set E defined on R^n and f \in \mathcal{C}^1(E) x' = f(x) where x(t_a) = x(t_b) and t_a,t_b \in I and where t_a < t_b. Show for n = 1, that the solution x is...

Homework Statement The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is v(r), where P is the pressure difference between the ends of the vessel and η is the viscosity of the blood. v(r) = P/4nl (R^2 - r^2) a) Find the...

Homework Statement Show that a sequence {a_n} is bounded if and only if there is an interval [c, d] such that {a_n} is a sequence in [c,d]. Homework Equations A sequence {a_n} is bounded provided that there is a number M such that |a_n| <= M. The Attempt at a Solution...

Homework Statement I'm working on trying to first to solve an ODE on the form \sqrt{x(t)}\frac{dx}{dt} = 2\cdot t^2 My task is to find a solution on the form x(t) =nt^s The Attempt at a Solution I do some separation and I get that the above is equal to \sqrt{x(t)} dx = 2...

Homework Statement In frame S, Herman drops a pizza at the same time that Pavel drops a marker. In frame S', Alice is moving relative to their S frame - What is the space time interval she sees? A. S' > S B. S' < S C. S=S Homework Equations Lorentz transformations is what we've been...

Homework Statement Let X be an ordered set where every closed interval is compact. Prove that X has the least upper bound property. Homework Equations X having the least upper bound property means that every nonempty subset that is bounded from above has a least upper bound, in other...

What is interval of definition of a solution of a Differential Equation? How can we find the interval of definition of a differential equation? What are the properties of this interval? Is the solution of the DE and DE itself are continuous and differentiable on the interval?

Homework Statement Find all values of θ in the interval 0 ≤ θ ≤ 360 that satisfy the equation sin 2θ = sin θ Homework Equations sin2θ = 2sinAcosA The Attempt at a Solution I'm a little confused on how to start off knowing sin2θ is equivalent to 2sinAcosA, would you factor this?

Hi All, So all closed interval [a,b] is compact (see Theorem 2.2.1 in Real Analysis and Probability by RM Dudley) Now, Let's say I have [0,10] as my closed interval. Let My Open Cover be (0, 5) (5, 7.5) (7.5, 8.75) (8.75, 9.375) ... Essentially, The length of each open...

I got a summer homework packet that covers all of last year's curriculum (Pre-Calc) and the first three chapters of next year's curriculum (Calc). I have no idea what I'm really doing with the calc stuff. I'm trying to teach myself sequences, limits, and derivatives. It was going pretty smoothly...

Homework Statement Homework Equations s2=c2(t2)-(x2) The Attempt at a Solution so.. s=72ly and t=100y c=c (72)2=(1)2(1002)-(x2) solving for x which is the distance i get x=69.39 aprox= 69. my question is when do we know to let c=1 or c=3*108 m/s how do we go back and forth between light...

Hello all, I always come across the technique of decomposing a real interval into intervals with rational end point, however, I am a bit confused with the half-open/half-closed cases. For example, [0,t) = \cup_{q < t, q \in \mathbb{Q}} [0,q) . And for the case of [0,t] , we can only...

Hello again. Sorry for all the posts. I have a histogram of frequencies in Mathematica and the intervals on the x-axis are predefined and kind of unrepresentative. I changed the bin number (with 'Histogram[mydata, binnumber]') but I can't seem to find anything on the internet about changing...

Im stuck in the 4 red boxes I've highlighted. 1st box: what is the method/quickest way to draw the graph? 2nd box: what does it mean by open interval? 3rd box: how would i sketch the preimage? what does preimage really mean? 4th box: how would i prove it for open interval...

Please show work. There was a negative sign that appeared in the solution and I don't know why. I know \sqrt{}(1-X) can be rewritten as (1-X)^1/2 and then you use the power rule to integrate but that gives you (1-x)^3/2 ------------ 3/2 2(1-X)^3/2 -------------- 3 My book shows...

I've tried proving the invariance of the spacetime interval from Lorentz transformations 3 times now, but every time I end up with two extra terms that don't cancel! Could I have some help?

Homework Statement Hi I have a position given by the point a vector v points to. Now I have a function, which is only defined for the points on and inside a circle with radius 2 within this point. Can I write this interval as x,y \in [(x-v_x)^2-(y-v_y)^2=4] ? Niles.

Hi, I am going through my notes trying to get things straight in my head and something is confusing me. I also have the feeling it will turn out not to be very complicated, which is why I am a bit frustrated with this. I know that there is something used in general relativity called the...

Homework Statement Find the interval of convergence of the series and, within this interval, the sum of the series as a function of x. \sum^{\infty}_{n=0}\frac{(x-1)^{2n}}{4^n} Homework Equations N/A The Attempt at a Solution Finding the interval is easy, using the ratio test it reduces...