intervals Definition and 276 Threads

Homework Statement We have C_n = [1-\frac{1}{n},2-\frac{1}{2n}] and C = C_1 \cup C_2 \cup C_3 \cup ... and are asked to describe the interval C and then prove that it is actually what we say it is. Homework Equations The Attempt at a Solution I am guessing that C = [0,2) and...

I was presenting my data on the Frank-Hertz lab to a lab class when I was asked by the professor why the interactions only happened in intervals of 4.9eV. Why weren't the free electrons exciting the mercury atoms to other energy levels? My answer was that I suspected at these temperatures and...

So the beginning of Rudin's Real and Complex Analysis states that the Riemann integral on an interval [a,b] can be approximated by sums of the form \Sigma\stackrel{i=1}{n}f(ti)m(Ei) where the Ei are disjoint intervals whose union is the whole interval. At least when I learned it, the Riemann...

I need to show the intervals where the wronskian is linearly independent and linearly dependent.. I don't know how to do that.. Here's what I have:

Homework Statement Obtain intervals x∈[0,α] for the existence of a unique solution dy/dx = f(x,y) = e^-(y-x)^2; y(0) = 0 on the rectangle B = [0,a]x[-b,b] Homework Equations The Attempt at a Solution Since both dy/dx and it's partial derivative of y are both continuous, a unique...

so i am hoping that all of you are familiar with the fact that a basic way of finding the distance between two points in 3d space is a^2+b^2+z^2=c^2. anyway i wanted to know in the equation ds^s=dx^2+dz^2+dy^2-(cdt)^2 does this show the distance between two points in in 3-d space including 1...

Homework Statement Find the local maxima and minima and sketch: Critical points: (3, -4) and (6, 0) Interval of increase: (3, ∞) Interval of decrease (-∞, 3) I'm not quite sure if I graphed this correctly since I wasn't given the function to doublecheck. The Attempt at a...

Let a and b be real numbers with a<b, and let x be a real number. Suppose that for each ε>0, the number x belongs to the open interval (a-ε, b+ε). Prove that x belongs to the interval [a, b].

Intersection of a sequence of intervals equals a point (Analysis) Homework Statement Let A_{n} = [a_{n}, b_{n}] be a sequence of intervals s.t. A_{n}>A_{n+1} and |b_{n}-a_{n}|\rightarrow0. Then \cap^{∞}_{n=1}A_{n}={p} for some p\inR. Homework Equations Monotonic Convergent Theorem If...

Working out of Boas' Mathematical Methods in the Physical Sciences; Chapter 14, section 2, problem 42... I'm supposed to write the power series of the following function, then find the disk of convergence for the series. Boas goes on to state, "What you are looking for is the point nearest...

Hello, Would it be correct to say that the function y=|(x^3)-1| is not monotonic, yet increases for every x>0 and decreases for every x<0? I hope one of you could comment. Thanks!

Hello, Homework Statement In which intervals is the floor function decreasing/increasing? Homework Equations The Attempt at a Solution I first presumed it was increasing for every integer x, now I am not sure. May anyone please confirm/debunk? Is it also monotonic for every...

Hello, Homework Statement I am trying to determine on what intervals the parabola y=ax^2+bx+c increases/decreases, without resorting to differentiation. Homework Equations The Attempt at a Solution For the function to be increasing on a certain interval f(x1)>f(x2) for any x1...

Let X1, X2, ... , Xn be a random sample from N(\mu, \sigma^2), where both parameters \mu and \sigma^2 are unknown. A confidence interval for \sigma^2 can be found as follows. We know that (n-1)S^2/\sigma^2 is a random varible with X^2(n-1) distribution. Thus we can find constants a and b so that...

Homework Statement If A and B are sets and f : A → B, then for any subset S of A we define: f(S) = {b ∈ B : b = f(a) for some a ∈ S} Similarly, for any subset T of B we define the pre-image of T as: f^{-1}(T) = {a ∈ A : f(a) ∈ T} Note that f^{-1}(T) is well defined even if f does...

Homework Statement y= (x^2 -7) e^xThe Attempt at a Solution I'm trying to find inflection points by setting the second derivative=0 I found that the derivative is: ##2xe^{x}+x^{2}e^{x}-7e^{x}=0## ##e^{x}[2x+x^{2}-7]=0## Then, the 2nd derivative: ##e^{x}[(x-1)(x+5)]=0##, then the inflection...

Homework Statement Find the intervals of increase and decrease of secx on the interval (-pi/2, 3pi/2). Homework Equations The Attempt at a Solution I found the derivative and set it equal to zero to get the critical points: f'(x)=sinx/cos^2x 0=sinx/cos^2x 0=sinx x= 0 and pi...

Homework Statement find the intervals of increase or decrease of the function f(x)= (3/(x^2+11)-1 i already find the 1st derivative f'(x)= -6x/ (x^2 +11). After that i didnt know how to proceed to find the interval. I need help for the solutions.

I wasn't sure if I should post this in the analysis or topology forum, but this seems to be closely related to compactness so I thought I'd post it here. When dealing with ℝ, the following theorem seems to be really important:"Every non-empty open set G in ℝ can be uniquely expressed as a...

Homework Statement [SIZE="3"]\sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+c}, where k is a positive integer.Homework Equations The Attempt at a Solution I found that it was discontinuous at [SIZE="3"]x = (-c)^{1/k}; and to determine if the sequence is decreasing, I took the derivative which is--I...

Homework Statement I need to prove that [0,1) and (0,1] have the same cardinality. My question is, do I have to define a function from [0,1) → (0,1] in order to show a correspondence or is there another method? Thanks.

Homework Statement The position versus time for a certain particle moving along the x-axis is shown in Figure 1. Find the average velocity in the time intervals 0 to 2 s, 2 s to 4 s, 0 to 8 s. Homework Equations The Attempt at a Solution I do not understand the question? I...

I have been tasked with solving the following inequality: \frac{1}{x} < 4 Attached to this thread is my attempted solution. As you can see I begin with simply solving the inequality for x, and I obtain the result x > \frac{1}{4} Next, I convert the equation into what I thought was the...

Homework Statement Prove that the σ-algebra generated by the collection of all intervals in Rn coincides with the σ-algebra generated by the collection of all open subsets of Rn. Homework Equations A σ-algebra is a nonempty collection Σ of subsets of X (including X itself) that is closed...

I am trying to find the three roots from x=0 to x=2∏ for this equation: x*Sin[x] + 1.5 x - 3. I want to divide the graph into intervals of say from x=1.0 to x=2.0 as one interval and so on and so forth. How do I go about inserting that code into my existing codes? I am using the bisection method...

Any resources you can recommend? Preferably online but I'm not against stopping by the library if need be. Thank you.

Maybe I'm getting a bit ahead of myself here, but for the sake of curiosity I'll ask it anyways. Is there any way that you can test when a function h(x) will have transcendental outputs vs rational or algebraic outputs? Specifically, if I have the following function f(x) = ssrt(x) Where...

Disclaimer: I am still learning physics. I think about weird things. This results in thoughts like the one that follows. My understanding of Planck length is that it is the smallest increment of length that can be measured, and to me this implies that an object can only be a whole number...

Hello physicsforum people, I'm not sure how many significant figures I should express a confidence interval to. I have confidence intervals for means that I need to express in a lab report, which I am going to do in the something ± something fashion. (I have assumed a normal distribution of...

When we use the nested interval property, we have closed intervals that are nested inside of each other and eventually when we do this a countable number of times out to infinity we eventually enclose a singlet point. So my question is can we apply this to the cantor set? I mean when we...

Homework Statement I have boundary conditions on my heat equation ## \dot{T}(x,t) = T''(x,t) ## ## T(0,t) = T(L,t), ## ## \frac{\partial T(0,t)}{\partial x} = \frac{\partial T(L,t)}{\partial x} ## Then at ## T= 0## ## T(x,0) = 1 ## for ## 0<x<L/4 ## ## T(x,0) = 0 ## for ## L/4<x<L ##...

Critical Points, intervals, local max/min help! Calculus. 1. I need help with a homework problem that I just cannot get right. It asks: Answer the following questions about the functions whos derivative is given below. f'(x) = (sinx +1)(2cosx +\sqrt{3} ), 0\leqx\leq2∏ a. what are the...

Dear all, I have a specification from a tool, which says, 80% of the reported measurements are within plus or minus 10% of the actual, at 95% confidence level. I am trying to make sense out of this statement. Assuming a normal distribution, please can someone tell me how to interpret...

I want to construct a premeasure on half open intervals in the set of extended real numbers and showing the steps of construction clearly. I know what is premeasure and half open interval of course, but I have problems with showing my steps clearly. Please help

If a rocket is traveling past the Earth at speed v, and the time interval measured by the astronaut is four times smaller than the time interval measured by an observer on the Earth. What is the value of v I have attempted the solution and got: Δt=γΔt' Where i believe that gamma will be...

What really are intervals in respect to functions ? As defined they are subsets of real numbers, for example, two numbers a,b belonging to R and a<b, so with that we can make out four intervals or sets with some variable x and treating a and b are inclusive or exclusive limits and also some...

Statistics question: I'm having trouble understanding my statistics professor's objection to this interpretation of confidence intervals. If you have some distribution with parameter x: X = Dist(x), and you perform a random experiment drawing N random variables from it, and derive from those...

Homework Statement Hi I have an equation as follows: f(x) = (2x-2.3)/(2x-5.29)^2 what i got for the derivative was: f'(x) = (-1.38-4x)/(2x-5.29)^3 Homework Equations f(x) = (2x-2.3)/(2x-5.29)^2 f'(x) = (-1.38-4x)/(2x-5.29)^3 The Attempt at a Solution what i got for the...

Homework Statement Suppose that f : ℝ→ℝ is continuous on ℝ and that lim f =0 as x→ -∞ and lim f =0 as x→∞. Prove that f is bounded on ℝ and attains either a maximum or minimum on ℝ. Give an example to show both a maximum and a minimum need not be attained. The Attempt at a Solution...

I have created 1000 random samples of size 10, where X~N(8,2). For each sample I have calculated the sample mean, sample variance, (sigma1)2 and (sigma2)2. I want to find a 95% confidence interval for the mean assuming the population variance is known, and a 95% confidence interval for the...

Homework Statement Define a function g on ℝ by f(x)=1/x if x < 0 and f(x)=-x if x≥0. Prove f is strictly decreasing on the intervals (-∞,0) and [0,∞), but that g is not decreasing on ℝ. Homework Equations The Attempt at a Solution I think I understand what I need to show, but I...

Homework Statement Suppose on a spacetime diagram, an event happens at x=-4, t=5 and another event happens at x=0 and t=6. If there is a frame such that the two events happen simultaneously, what would the relative speed of that frame be? Homework Equations The Attempt at a...

Homework Statement Assume the nested Interval property it true and use a technique similar to the one used to prove the Bolzano Weierstrass theorem, to give a proof of the axiom of completeness. axiom of completeness: Every non-empty set of reals that is bounded above has a least upper bound...

Improper Integrals -- Infinite Intervals Homework Statement Evaluate the integral. (from e to infinity) ∫(25/x(lnx)^3)dx Homework Equations The Attempt at a Solution I know that for evaluating improper integrals, you can take the limit as t approaches infinity of the given...

Let $\alpha$ be a real number between 0 and 1 written in binary: e.g., $\alpha=.1011001\ldots$ means $\alpha=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^4}$$+\frac{1}{2^7}+\ldots$ Make a set of nested intervals by starting with $I_0=[0,\ 1]$, then defining recursively $I_n$ to be the (closed) left...

Homework Statement I understand about everything except why the b and a values on the integral change from 0,3 to 9,36

Homework Statement It might not be a real topology question, but it's an exercise question in the topology course I'm taking. The question is not too hard, but I'm mainly doubting about the terminology: Homework Equations N.A. The Attempt at a Solution I would think not, unless I'm...

Just a quick question on spacetime intervals in spacetime. Why is the spacetime interval between two events given by Δs^2 = -c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2, rather than c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2 (as if it were the distance between two points in four spatial dimensions)? Or more succinctly...

Am i right in saying i can use this formulae: - W/EI((x^3/12) - (xL^2/16)) + w/EI((Lx^3/12) - (x^4/24) - (xL^3/24)) please help. See attached question. Question aii. Thanks

Homework Statement I need to show that [0,1] and [0,2] have the same cardinality by giving a formula for a function that is bijective. Aren't there a number of functions that can fit this description? Can I then use any one? I'm a little confused, my teacher didn't really elaborate much upon...