Continuous Definition and 1000 Threads

Hi there! I got some difficulty understanding a question regarding electrons Electrons which are initially at rest are subjected to a continuous force of 2E-12 N along a length of 2 miles and reach very near the speed of light. a) Determine how much time is required to increase the...

Homework Statement Let I be an interval in R, and let f: I-->R be one-to-one, continuous function. Then prove that f^(-1):f(I)-->R is also continuous. Homework Equations The Attempt at a Solution I started a thread yesterday and had some responses but the proofs became quite...

Homework Statement Let I be an interval in the real line, and let f map I --> R be a one-to-one, continuous function. Then prove that f^(-1) maps f(I) --> R is also continuous The Attempt at a Solution I've started with the definition of continuity but I don't see where to go next.

Homework Statement With knowledge of the orthogonality conditions for eigenfunctions with discrete eigenvalues, determine the orthonormal set for eigenfunctions with continuous eigenvalues. Use the definition of completeness to show that | a(k) |^2 = 1. 2. The attempt at a solution The first...

Hello! Could anybody give me an idea about this proof? knowing f_{i}:X\rightarrowR i=1,2 to show whether f_{3}=min{f_{1},f_{2}} is continuous! Thanks in advance, Regards

Homework Statement Give an example of a function f : R -> R where f is continuous and bounded but not uniformly continuous. Homework Equations A function f : D -> R and R contains D, with Xo in D, and | X - Xo | < delta (X in D), implies | f(X) - f(Xo) | < epsilon. Then f is continuous...

Hi, I am having some problems understanding the degree of a continuous map g:circle --> circle I have found a definition in Munkres (pg 367) that I can't really understand (I'm an engineering student with little algebraic topology) and one in Lawson (pg 181), Topology:A Geometric approach...

I have an assignment question " let (X,d) be a metric space. a is element of X. Define a function f maps X -> R by f(x) = d(a,x). show f is continuous." I'm not sure what this function looks like. Is f(x) = sqrt(a^2+x^2) and if it is I need abs(x-a) < delta?? I'm confused.

What device (thing with at least one moving part) in constant motion, has given the longest service?

Homework Statement An ambulance travels back and forth, at a constant speed, along a road of length L. At a certain moment of time an accident occurs at a point uniformly distributed on the road. (That is, its distance from one of the fixed ends of the road is uniformly distributed over...

Homework Statement Find a continuous surjection from [0,1) onto [0, infinity) Homework Equations The Attempt at a Solution I have only been able to come up with one mapping but then I realized it did not work. Any help would be appreciated.

41. Find the Horizontal Asymptotes for17x/(x^4+1)^1/4 The answer I got is 17 and –17 . Can anyone correct me if I’m wrong? 62. f(x)= 4x^3+13x^2+11x+24 / x+3 when x<-3f(x)= 3x^2+3x+A when -3 less than or equal to xWhat is A in order for it to be continuous at -3?I don’t understand the top...

Find the values of a and b that make f continuous everywhere?? 1. Find the values of a and b that make f continuous everywhere?? Homework Equations f(x)=\begin{cases} \frac{x^2-4}{x-2}&\text{if } x\x<2\\ ax^2-bx+3 &{if} 2<x<3\\ 2x-a+b&\text{if } x\geq 3\end{cases} The Attempt at a...

Let I be the interval I=[0,infinity). Let f: I to R be uniformly continuous. Show there exist positive constants A and B such that |f(x)|<=Ax+B for all x that belongs to I. Please help me!~

Homework Statement Let I be the interval I=[0,infinity). Let f: I to R be uniformly continuous. Show there exist positive constants A and B such that |f(x)|<=Ax+B for all x that belongs to I. 2. The attempt at a solution Proof by contradiction.

Homework Statement Assume f is a continuous real function defined in (a,b) such that f(\frac{x+y}{2})<=\frac{f(x)+f(y)}{2} for all x,y in(a,b) then f is convex. Homework Equations The Attempt at a Solution my attempt is to suppose there are 3 points p<r<q such that f(r)>g(r)...

Man I hate probability...anyhow could some help me with this Q as I am not understanding how to set it up... Suppose that the force acting on a column which helps to support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips: What is the probability...

Hey guys, I'm having trouble doing ct convolution i'm trying to convolve two signals together ie, the input x(t) and the impulse response h(t). basically, knowing the impulse response of an LTI system, you can find out the response y(t) to any arbitrary input x(t) using the convolution...

Homework Statement When a function is piecewise smooth, then f and f' (the derivative of f) are piecewise continuous. In my book they mention "a function f, which is continuous and piecewise smooth". How can f be both continuous and piecewise continuous?

First of all, hello everyone, this is my first post so I am not sure if this the right place to post this question. I am wondering if anyone can help me understand this question better. The question goes as: if f is continuous on [a,b], f(x)>0, and f(x0)>0 for some x0 in [a,b], prove...

I'm in need of sources, articles, mainly anything that can provide information on finding the exact number of zeros for any given continuous function, thanks in advance.

Q. Determine the constants a and b so that the function is continuous on the entire real line. 2 if x <= -1 f(x) = ax+b if -1 < x < 3 -2 if x >= 3 Ans: a = 1; b = -1 I wonder if the answer is right??

Well, my first question was answered so I figured I would post the second problem I had problems with. It is: f(x) = lim _{n->\infty}\frac{x^{2n} - 1}{x^{2n} + 1} Where is f continuous? My first thought is that it is continuous everywhere since I can't find an x value that would make the...

Homework Statement Hey. How can I show that this is a Continuous function? Homework Equations The Attempt at a Solution

Homework Statement If f is a continuous mapping of a metric space X into a metric space Y, Let E be any subset of X. How to show, by an example, that f(\overline{E}) (\overline{E} is the closure of E) can be a proper subset of \overline{f(E)} ? And is there something wrong with my attempt...

Homework Statement For what value of the constant c is the function f continuous on (-\infty,\infty) f(x)=\left\{\begin{array}{cc}cx^2+2x,&\mbox{ if } x<2\\x^3-cx, & \mbox{ if } x\geq2\end{array}\right. Homework Equations No idea :( The Attempt at a Solution I tried looking...

can you example a function that is continuous at every point but not derivable

Here is a mystifying question from Rudin Chapter 4, #15 Call a mapping of X into Y "open" if f(V) is an open set in Y whenever V is an open set in X. Prove that every continuous open mapping of Reals into the Reals is monotonic. I'm having trouble proving this, in part, because I don't even...

Homework Statement A thin rod bent into the shape of an arc of a circle of radius R carries a uniform charge per unit length lambda = 2.20×10-9 C/m. The arc subtends a total angle 2 theta0, symmetric about the x axis, as shown in the figure below. theta0 = 28.0° and R = 0.28 m Hint: hard to...

Does the expansion of Space require continuous energy?? I'm curious; does the expansion of Space require energy? I'm assuming that the expansion of space must have some kind of 'momentum' (the big bang must have required an input of inertial energy directly into the geometrical expansion of...

I understand and agree that an electron is only a name for a continuous wave that has collapsed because of an observation or other perturbation. Where observations may be made with electric fields, magnetic fields, or both which cause the collapse the continuous wave. But what I don’t...

It can be shown that if F has continuous 2nd partials, then div curl F = 0. According to Stoke's Theorem, the work done around a closed path C is equal to the flux integral of curl F on a surface sigma that has C as its boundary in positive orientation. However, this integral is equal to the...

Homework Statement assume h: R->R is continuous on R and let K={x: h(x)=0}. Show that K is a closed set. Homework Equations The Attempt at a Solution since we know h is continuous and h(x)=0. therefore, we know there is a epsilon neighborhood such that x belongs to preimage...

What is Meant by Time & Space Being "Continuous"? Hi All, Can someone tell me what is meant by time & space being "continuous" as opposed to "discontinuous"? What exactly does this mean in laymen terms and is time & space being "continuous" a widely-accepted "theory" or is this what we may...

Homework Statement Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2} The Attempt at a Solution I just proved in the first part of the question, not posted, that...

[SOLVED] continuous at irrational points Homework Statement Every rational x can be written in the form m/n where n>0, and m and n are integers without any common divisors. When x = 0, we take n=1. Consider the function f defined on the reals by f(x) = 0 if x is irrational and f(x) = 1/n if x...

A parametric equation, say r(t), is smoothly parametrized if: 1. its derivative is continuous, and 2. its derivative does not equal zero for all t in the domain of r. Now that sounds simple enough. Now let's say we have the tractrix: r(t) = (t-tanht)i + sechtj, ... then r'(t) = [...

what does continuous almost everywhere - alpha means? I know that the term almost everywhere means that the property holds everywhere on the measurable space except on a subset of measure 0,what I don't really understand is the term almost everywhere-alpha.

Homework Statement Let Ce([0,1], R) be the set of even functions in C([0,1], R), show that Ce is closed and not dense in C. Homework Equations The Attempt at a Solution I think I can solve this if I can show that even functions converge to even functions, but I can't quite...

Homework Statement For a particle moving in a potential V(x), what are plausible forms of V(x) that give: (i) entirely continuous, (ii)entirely quantised (iii) both continuous and quantised energies of the particle? Sketch, with justification, the forms of V(x) for each of...

Hi, I think I've gotten this problem, but I was wondering if somebody could check my work. I still question myself. Maybe I shouldn't, but it feels better to get a nod from others. Homework Statement Consider the space of functions C[0,1] with distance defined as...

Homework Statement A mapping f from a metric space X to another metric space Y is continuous if and only if f^{-1}(V) is closed (open) for every closed (open) V in Y. Use this and the metric space (X,d), where X=C[0,1] (continuous functions on the interval [0,1]) with the metric d(f,g)=\sup...

H = [a,b]\times[c,d] . f:H\rightarrowR is continuous, and g:[a,b]\rightarrowR is integrable. Prove that F(y) = \intg(x)f(x,y)dx from a to b is uniformly continuous. I initially ripped g(x) and f(x,y) apart and tried to show each was continuous. This failed. In short, I am...

Hey... I have a quick question for you guys about electric potential. I have a spherical shell with a constant charge distribution. The total charge(Q), along with the shell's radius is given. Also, V(infinity) is defined to be 0 in this case. I'm told to find: a. The potential at r = the...

Homework Statement f(x,y) = 1/(x^2 + y^2 -1) 1. For what domains is f continuous? 2. For what domains is f a C^1 function? (Here C^1 means that the first derivatives of f are all continuous) Homework Equations The Attempt at a Solution I would be very grateful for the help...

Homework Statement Problem statement is underlined. Having problems to prove this. Homework Equations F(x) = ∫ f(x) dx Question relating to cumulative distributive function. Part ii requiring to relate cumulative distributive function to probability density function. The Attempt...

This is a question from Papa Rudin Chapter 2: Find continuous functions f_{n} : [0,1] -> [0,\infty) such that f_{n} (x) -> 0 for all x \in [0 ,1] as $n -> \infty. \int^{1}_{0} f_n dx -> 0 , but \int^{1}_{0} sup f_{n} dx = \infty. Any idea? :) Thank you so much!

Homework Statement For each a\in\mathbb{R}, find a function f that is continuous at x=a but discontinuous at all other points. The Attempt at a Solution I guess I am not getting the question. I need to come up with a function, I was thinking of a piecewise defined one, half rational...

1. A nonconducting rod of length L = 6cm and uniform linear charge density A = +3.68pC/M . Take V = 0 at infinity. What is V at point P at distance d = 8.0cm along the rod's perpendicular bisector? 2. V = S E * ds One half of the rod = L/2 1/4piEo = 9x10^9 R = sqrt((L/2)^2 +...

If f is a real function on R^1, and holds:lim [f(x+h)-f(x-h)] = 0 for every x belongs R^1. Does f continuous? And I thought it no. Since I considered it mentioned only the left-hand and right-hand limit are equal, but whether or not equal to f(x) was not exactly known. Will anybody provide...