Domain Definition and 704 Threads

I am reading a graduate-level Abstract Algebra lemma on noetherian integral domain, I am bring it up here hoping for help. The original passage is in one big-fat paragraph but I broke it down here for your easy reading. Let me know if I forget to include any underlying lemmas, and especially...

I'm having trouble evaluating this surface integral. This would be very simple to solve if the parameter domain of the variables u and u was a square region. However, that isn't the case here. I've tried using a change of variables and saying that u = r cos x, and v = r sin x. Where 0 < x < 2pi...

Hello everyone, Here is the definition of path connected and domain my textbook provides: Definition 171. An open set S is path connected if each pair of points in S can be connected by a polygonal line (e.g. a finite number of line segments connected end to end). A domain is an open set that...

I need to find the domain of this function: $$f(x) = \frac{1+x}{ e^{cos(x)}}$$ I set $${ e^{cos(x)}}> 0$$ But I'm not sure what to do after this.

In Alaca and Williams' (A&W) book: Introductory Algebraic Number Theory , Theorem 1.2.1 reads as follows:Without any earlier definition or clarification, A&W refer to $$a/p$$ and $$b/p$$ (see text above) ... BUT ... how should we regard such elements? What exactly do they mean and how do we...

Homework Statement Given the Functions f(x)=4x-1 g(x)=3-2x^2 h(x)= sqrt (x+5) What is the domain of h(g(x))? Homework Equations the subject is finding the domain of a composite function The Attempt at a Solution I don't understand what I have to 'bring over' from g(x). I think x cannot equal...

Find the domain of the equation $$1 \ne e^{1-x^2}$$ Is there a way to evaluate this function?

I need to find the domain of this function.$$h(x) = 1 / \sqrt[4]{x^2 - 5x}$$ So, I understand that I need to set $$x^2 -5x > 0$$ from that I get $$ x(x-5) > 0$$ and $$ x > 5$$ However, the answer in the textbook is given: $$ ( \infty, 0) \cup (5, \infty)$$ Which mean that the graph has a...

I've always been having trouble with the domain and range of inverse trigonometric functions. For example, let's start with an easy one: $\sin^{-1}\left({x}\right)$ Process: First, I draw out the function of $\sin\left({x}\right)$. Then I look at its range and attempt to restrict it so that it...

¿domain and asinptotestotes of x^2y+xy^2 = 2? Answer (inf -2]U(0, inf +) asinptotes AV x = 0 AH y = 0 Oblique x-y = 0 I can isolate y or i mean solving for y

Homework Statement There are two vertical ovals, one containing the x-coordinate values and one containing the y-coordinate values. The x-axis values: -1, 8, 0 and the y-axis values: -4, 0, -1 (-1,-4) (8,0) and (0,-1) are the three points. Homework Equations I'm not sure this is an equation...

Homework Statement This integral is actually part of a question I had on an exam about analytic continuation. The integral is \int_0^1 dx \frac{x^n}{\sqrt{x^3+5}} . The first part of the question is "what is its domain of validity for absolute convergence of the integral?" It then goes...

In...... it has beenshown in an elementary way that is ... $\displaystyle\int_{0}^{\infty}\frac{\ln x}{x^{2}+a^{2}}\ dx = \frac{\pi\ \ln a}{2\ a}\ (1)$The integral (1) isvery useful to shed light on the behavior of the logarithm functionin the complex field. Let's suppose we want to solve the...

Hello all, First, congratulations on the quick LATEX bar on the side, will try it now the first time. I am looking for the domain of \sqrt{sin(\sqrt{x})} I need that the expression under the square root will be non-negative. The expression involves sin. The sin function is non-negative at...

I am reading Joseph Rotman's book Advanced Modern Algebra. I need help with Problem 2.21 Part (i) on page 94. Problem 2.21 Part (i) reads as follows: -------------------------------------------------------------------- Let $$R$$ be a domain. Prove that if a polynomial in $$R[x]$$ is a unit...

Hello people of Physics Forums, In my research into transmission lines, I have come across the following function: x = ( a - i * b * tan(t) ) / ( c - i * d * tan(t) ) In the above equation x, a, b, c and d are complex and t is real. If my analysis is correct, varying t from -pi/2 to...

Hi I have the function I have worked out the domain as not equal to 1 using the fact the denominator can't equal 0. Now I am stuck finding the range. How would I find it without graphing. The answer is y<0 , y=>3.

We can view the amplitude vs time variation of an EM wave using an oscilloscope with the needed bandwidth. Such a view shows us the shape of the wave (sinusoid or other), the number of cycles contained in a given burst, any modulating signal etc. Though it wouldn't be measured with an...

Homework Statement Let ## S = \{ (m,n) : m,n \in \mathbb{N} \} \\ ## a.) Show function ## f: S -> \mathbb{N} ## defined by ## f(m,n) = 2^m 3^n ## is injective b.) Use part a.) to show cardinality of S. The Attempt at a Solution a.) ## f(a,b) = f(c, d ) ; a,b,c,d \in \mathbb{N} \\\\ 2^a...

What is 'Quantum Domain'? I read something about it being a level of existence... If it is a level of existence, what sort of classification of existence are we talking about?

Hello all, I am trying to determine if the domain of the function: \[f(x,y)=\frac{\sqrt{ln(x^{2}+y^{2}+1)}}{\left | x \right |+\left | y \right |+\sqrt[4]{xy-1}}\] Is an open set or closed set and if it's bounded. The domain is in the attached graph. The book say it is closed and...

Homework Statement I am given the following dynamic system. I want to find the transfer function, θ1(s)/T(s). The main body of the satellite, J1, acts like a large mass flying through space; space is essentially without friction and therefore no damping is imparted on the main body...

Homework Statement For vi(t) =V0 cosωt, obtain an expression for vout(t) in the circuit below and then evaluate it for V0 = 4 V, ω = 400 rad/s, R = 5 kΩ, and C = 2.5 μF. Homework Equations The Attempt at a Solution For this problem, I am having difficulty taking that second term...

Hi all, It is well know that, rectangular or quadrilateral element gives better result over triangular meshes in finite element method. I know, Rectangular meshes has more discretization error, but my question is that, if i refine mesh up to 4 to 6 pixel width of screen, where i am wrong?

Hi Folks, Have a task , but no idea how to resolve. Will appreciate any help. Consider the function f: {5,6,7} →{A,B,C} given by f(5)=A, f(6)=C, and f(7)=B Draw its arrow diagram and state its domain, codomain and range. Is it (i) onto and (ii) one-to-one ? Explain. Does it have...

Homework Statement Homework Equations How do you find the domain? The Attempt at a Solution I figure (1,10) makes sense because it can't be 0 because its needs a quantity to exist. Right? I see they came up wit 5, but how did they get 5 exactly? They say its just because its...

Homework Statement Where Vs = 120 ∠0° V Homework Equations All values are represented in ohms, so they are treated as resistors. The Attempt at a Solution Series inductor + resistor 30+j10 ohms = 31.62∠18.435° Parallel resistor and inductor+resistor (1/50)= 0.02∠0°...

Hi, Are there any open source C or Fortran libraries for solving 3D Poisson'sequation on an irrefular domain? I'm having difficulty finding them. If not, is there any papers or recipes that would be useful so I could write my own? Speed is not a priority, I just need anything that works...

I understand that the Fourier transform maps one function onto another. So it is a mapping from one function space onto another. My question is, why is it often referred to as a mapping from time domain to the frequency domain? I don't understand why the image of the Fourier transform...

So I have this question: After screen-shotting it I realized I added instead of subtracting, so my answer to the first part is about 4.7...is that right? The second part I'm not sure at all how to find the equation for the derivative of the curve.. when I don't have the equations for h(x)...

Let ##M## and ##N## be smooth manifolds and let ##F:M \to N## be a smooth map. Iff ##(U,\phi)## is a chart on ##M## and ##(V,\psi)## is a chart on ##N## then the coordinate representation of ##F## is given by ##\psi \circ F \circ \phi^{-1}: \phi(U \cap F^{-1}(V)) \to \psi(V)##. My question is...

Homework Statement Find the Laplace transform of f(t) = t \forall 0≤t≤T, 0 otherwise Homework Equations The Attempt at a Solution I write the function as tu(t)-t*u(t-T) That is turn on the function t at t=0 and turn the function t off at t=T. It seems to be right to me...

Problem statement Given sin theta (sqrt 3)/2 Determine the domain for the following solution https://www.physicsforums.com/attachments/655052) determine each general solution using the angle measure specified. Revelant equations Attempt at solution1What is the reasoning behind that? For...

Let's say f(x) = sqrt(x-1) And g(x) =x^2 What is the domain of f(g(x)) Well the domain of g(x) is all real numbers and the equation for the new function is sqrt(x^2-1) Am I right to say that the domain for f(g(x)) is x greater than or equal to 1 and less than and equal to -1??

Homework Statement Prove that there is a constant C such that arctan\sqrt{\frac{1-x}{1+x}} = C - \frac{1}{2}arcsinx for all x in a certain domain. What is the largest domain on which this identity is true? What is the value of the constant C? The Attempt at a Solution Now I know how...

Hello all, I am trying to find and draw the domain of this function: \[f(x,y)=\sqrt{ln(\frac{9}{x^{2}+y^{2}})}\] Somehow I find some technical difficulty with it. I have found 3 conditions: \[\ln \left ( \frac{9}{x^{2}-y^{2}} \right )\geq 0\] and \[\frac{9}{x^2-y^2}>0\] and \[x^2\neq...

This question is from the parametric equations chapter of my calc book. I am given x =\frac{1}{\sqrt{t+1}} and y = \frac{t}{t+1}, for (x> -1) Solving the x(t) for t, we get \frac{1- x^{2}}{x^{2}} Eliminating the parameters by substitution, we get y = 1 - x^{2} for (x > 0) My question is...

Hello people, i need help with frequency domain study in electric current shell modul. I have one IDC and i have electrodes from gold, and i don't know what should i do to see my frequency response on diagramm? Does anyone has any idea?

Homework Statement Find the domain and range of (f+g)(x) Given that F(x)= 1/(x-1) and g(x) = sqrt(x) Homework Equations The Attempt at a Solution I added the two functions to get 1/(x-1) + sqrt(x) To get domain, i look at the restrictive x values for both to get x greater than 0 and not...

My teacher discussed an in and out method that could be used however I don't understand how that works. Can someone explain it to me? The teacher said this method would allow us to determine the domain and range without knowing what the graph looked like. How I have been doing it is looking at...

state the domain $$y = x\sqrt{1 - x^2}$$ so $$1 - x^2 >= 0$$ $$-x^2 >= -1$$ $$x^2 <= 1$$ $$d = {x <= (+)(-) 1}$$ or should I say $$d = {-1, 1}$$ which one is correct?

Homework Statement X(w) = 3cos(2w) + 2 sin(3w) calculate x(n) Homework Equations x(n) = (1/2pi) ∫ X(w) e^(jwn)dw The Attempt at a Solution When integrating over 0 to 2 pi, my answer is 0. Which would not be the case.

Homework Statement I'm having a problem with solving the domain of |x^2+y^2|<=|z^2|. Homework Equations The Attempt at a Solution From what I got this should be separated into two expressions: x^2+y^2<=z^2, and x^2+y^2>=-z^2. The later doesn't have a real solution because of the...

I'm working on a problem and one part of it is finding the zero-input response of a system in the frequency (or "s") domain. The zero-state response can be easily found in the frequency domain, it's just: Y_{zs} = X(S)H(S) But I can't for the life of me find the equation for calculating...

Anyone have an idea to find a first and second natural frequency from time domain and frequency domain plot resulting from an accelerometer measuring the vibration in cantilever beam ? Thanks very much :)

Hello to all: I was trying to solve the following question: what is the domain of the function y = log [(4-t)^(2/3)] for Real t. Here is my reasoning: The domain of the log(x) is x>0. I would have interpreted this question in terms of the log of the cubic root of (4-t)^2. Thus, I was...

Hi I'm having some problems with an task in my class. It's as follows Given the real function f(x)=Xx for X ∈ (0,∞). Then I'm to expand the definition area to [0,∞), f shall still be continuous. What does f(0) have to be? Thanks for any help :)

Homework Statement Find the domain of following functions : Note: [.] denotes greatest integer function. {.} denotes fractional part of a function. 1. f(x)=sin-1([x]/{x}) 2. √(2{x}2-3{x}+1) 3. Solve the equation : y=[sinx+[sinx+[sinx]]]/3 [y+[y]]=2cosx Homework Equations...

How can I integrate this expression: \[ \int_0^{\infty} \mathcal{J}_1(kR)e^{-kz}dk = \frac{1}{R} \left[1 - \frac{z^2}{\sqrt{R^2 + z^2}} \right] \] where \(\mathcal{J}_1\) is the Bessel function of order 1.

Is anyone familiar with plotting an infinite domain PDE where the solution is an integral. Take the solution \[ T(x,t) = \frac{100}{\pi}\int_0^{\infty}\int_{-\infty}^{\infty} \frac{\sinh(u(10-y)}{\sinh(10u)} \cos(u(\xi-x))d\xi du \] How could I plot this in Matlab, Mathematica, or Python? As a...