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.
Homework Statement
Suppose that a discrete-time signal x[n] is given by the formula
x[n] = 10cos(0.2*PI*n - PI/7)
and that it was obtained by sampling a continuous signal at a sampling rate of fs=1000 samples/second.
Determine two different continuous-time signals x1(t) and x2(t)...
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
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...
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...
Let X be a compact space, (Y,p) a compact metric space, let F be a closed subset of C(X,Y) (the continuous functions space) (i guess it obviously means in the open-compact topology, although it's not mentioned there) which satisifes:
for every e>0 and every x in X there exists a neighbourhood U...
Homework Statement
How is the theorem "Continuous functions have closed graphs" proven in the setting of a general topological space? (assuming the theorem is still valid?)
Is there a continuous function f(x) defined on (-\infty,+\infty) such that f(f(x))=e^{-x}?
My opinion is "no", and here is how i think:
first of all if such a function exists, it should be a "one-to-one" function, that is for every y>0, there should be exactly one x such that f(x)=y.
Thus by...
Dear friends,
I just joined the forums, and I'm looking forward to being a part of this online community. This semester, I signed up for Analysis II. I'm a math major, so I should be able to understand pretty much everything you say (hopefully). However, I'd really appreciate it if you try...
Dear friends,
I just joined the forums, and I'm looking forward to being a part of this online community. This semester, I signed up for Analysis II. I'm a math major, so I should be able to understand pretty much everything you say (hopefully). However, I'd really appreciate it if you try...
[SOLVED] The continuous dual is Banach
Homework Statement
I'm trying to show that the continuous dual X' of a normed space X over K = R or C is complete.
The Attempt at a Solution
I have shown that if f_n is cauchy in X', then there is a functional f towards which f_n converge pointwise...
I'm having trouble with the third part of a three part problem (part of the problem is that I don't even see how what I'm trying to prove can be true).
The problem is:
Let X and Y be topological spaces with X=E u F. We have two functions: f: from E to Y, and g: from F to Y, with f=g on the...
Homework Statement
This is not a homework question. I am solving this from the lecture notes that one of my friend's has got from last year.
If C(X) denotes a set of continuous bounded functions with domain X, then if X= [0,1] and fn(x) = x^n. Does the sequence of functions {fn} closed ...
Homework Statement
Suppose that fk : X to Y are continuous and converge to f uniformly on every compact subset of the metric space X. Show that f is continuous.
(fk is f sub k)
Homework Equations
Theorem from p. 150 of Rudin, 3rd ed:
If {fn} is a sequence of continuous functions on E...