Domain Definition and 743 Threads

does the Dirac measure still exist with complex variance? The Dirac delta function can be rigorously defined as a measure. See http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure For the gaussian form of the Dirac delta function we have, \[ {\rm{\delta (x - x}}_0 ) =...

6throute (x-7) -------------- log11(13-x) What is the domain of the function in interval notation. I know to set x-7 > 0, so that gets me x>7 , and I know I have to set 13-x > 0, which gets me x < 13. But the notation that is correct is [7,12)U(12,13). Where do you...

Homework Statement Hi If I have a function defined in one point only given by e.g. f(x) = 2, then is the function f defined on a open "interval" or a closed "interval"?

hi everybody, i'd like to discuss with you a problem occurred to me in the study of a central symmetry field in non rel. qm. at a certain point, i get the linear operator P_{r}^{2}=\frac{1}{r}\frac{\partial^{2}}{\partial r^{2}}r , which is the square of radial momentum, and i want to determine...

¿what is the domain of validity of inverse square laws of Newton and coulomb? I think (correct me if this is false) that at the small scale these laws have been verified accurately , but ¿what happens with large distances? :rolleyes: . ¿Have been done an experiment which measured the...

Homework Statement Prove that if every continuous real-valued function on a set X attains a maximum value, then X must be compact.Homework Equations None really.The Attempt at a Solution None really, not sure where to start. I know that if a space is compact, every function attains it's minimum...

Problem: Assume that f: [0,infinity) -> R is continuous at every point of its domain. Show that if there exists a b>0 so that f is uniformly continuous on the set [b,infinity) then f is uniformly continuous on [0,infinity). I don't really know where to start with this one, any help would...

Homework Statement What is the domain of the following function? f(x,y) = (\sqrt(x) + x\sqrt(y)) \sum_{k=1}^{\infinity} (k^3 + k) x^k y^k when D_f \subset \Re^2 . The Attempt at a Solution The domain is x>0 \in \Re and y>0 \in \Re in my opinion.

Homework Statement What is the domain for tan(x/b)? Homework Equations The Attempt at a Solution tan(x) domain is all real number , except x=\pi/2+n pi nEI tan(x/b)will be bpi/2+bnpi? Is there any form i can write? Am i right? Thanks

[b]1. Find absolute max/min for the given function with the specified domain. f(x,y)= x^2-xy+y^2 on the circular disk x^2+y^2 less/equal 4, use parametrization when checking boundary. [b]2. f(x,y)= x^2-xy+y^2 x^2+y^2 less/equal 4 [b]3. The only thing I...

Homework Statement f(x) = x + 1 D=[-9, 9] g(x) = x2 D=(1, 5) Question to be solved Find both g o f and f o g and specify their domains The attempt at a solution g o f = (x+1)2 This is where I don't really know what to do, however I'll let the logical part of my brain go a bit...

I face some difficulties to find the domain Now i put my questions and please help me to answer it i try solve it thanks

Find the range of the equation. f(x)=x²+4Things I know for sure: x²>=0 We are brushing up on functions and interval notation in my calc class, and I can't remember how to do this in interval notation. If x is a number being squared it has to be positive or zero. So at the minimum the answer is...

Homework Statement Find domain of \sum_{n= 0}^\infty \frac{(-1)^{n}x^{2n}}{2^{2n}(n!)^{2}} Homework Equations The Attempt at a Solution I set it all up but I can't really seem to simplify it. \frac{(-1)^{n+1}x^{2(n+1)}}{2^{2n+2}(n+1)!^{2}}\bullet\frac{2^{2n}(n!)^{2}}{(-1)^{n}x^{2n}}

1. Find the domain of f(g(x)) where f(x)= radical 25-x^2 and g(x)= ln(x+3) 2. For the domain of f I got x < or equal to +/- 5 and for the domain of ln(x+3) I got x+3 > 0 3. (0, 145) Thanks for your time. :P

Homework Statement f(x) = e^{x}cos(x) has the domain [0, 2*pi] (a) Find the absolute maximum and minimum values of f(x). (b) Find the intervals on which f is increasing. (c) Find the x-coordinate for each point of inflection of the graph of f. No calculator use allowed. Homework...

Homework Statement Form the composition f o g o h and give the domain. f(x) = x - 1, g(x) = 4x, h(x) = x2 Homework Equations The Attempt at a Solution f(g(h(x))) = 4x2-1 The domain of x is any real number.

Homework Statement For the following questions, find the Domain and Range. Use either the graph or turning point method. Homework Equations 1. y= -x+6x-8 2. y= x^2-3x-5 3. y= -x^2+4x+4 And a question on the matter, when you complete the square, as in when I half the middle term...

My question is best stated by using an example: Suppose f is a function defined only for rational x, and for rational x f(x) = 1. Say we want to prove that f is continuous at x = 1. Then we want to show that for every positive epsilon there exists a delta > 0 such that |f(x) - f(1)| <...

Homework Statement prove that: \vec{F} = \frac{-y^2}{(x-y)^2}\vec{i} + \frac{x^2}{(x-y)^2}\vec{j} is a conservative field, and find the potential in the domain: D: (x+5)^2 + y^2 \leq 9 Homework Equations ? The Attempt at a Solution Well, \frac{\partial P}{\partial y} =...

When solving Laplace's equation over a triangular domain. Why is it a good idea to take M = N?

Find the domain and range of y=sin^2x I have a hard type computing this into my graphing calculator. Can someone help in the steps to find the domain?

Homework Statement determine if a) f(z) = e^z / (z^2 + 4) b) f(z) = conj(z) / |z|^2 c) f(z) = sum from 0 to inf. [ (e^z / 3^n) * (2z - 4)^n ] is analytic and sketch the domain where it is analytic. Homework Equations The Attempt at a Solution a) i don't know how to separate the...

Homework Statement Find all the natural domain of the function algebraically, and confirm that your result is consistent with the graph produced by your graphing utility. h(x) = 3/2-cosx Homework Equations (a) h(x) = 3/2-cosx (b)x2-1/(x+1) The Attempt at a Solution Do I need to...

Homework Statement Find the domain of the function. You will need a sign graph. Answer in interval notation. Homework Equations f(x)= (3)/[(x2-4x)1/2] The Attempt at a Solution No clue - I don't know how to use a sign graph or what the positive/negative results mean as solutions on a number line.

Suppose you have f(x) = ( x^2 + 4x + 3 ) / (x+3), making a scan in that function you can say that D : R / x =! -3, because x with -3 would give a division by zero. But, suppose you simplify that function by factorizing, you get f(x) = x + 1 It would represent the same value, but my teacher...

Here is my question, that what is the domain of f, while f(x,y)=1/(x-y2)

A = (0, infinity), B = C = D = R where R is all real numbers f: A->B, g: B->C, h: C->D f(x) = lnx, g(y) = 3y, h(z) = e^z h o g o f ? -------------------------------------------- For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g o f) ⊆ domain(h) So g o f should be...

For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g) ⊆ domain(h) Is that correct? So R ⊆ R for 1, and R ⊆ R for the other so it is ok? --- Second question: but how can you have the function h with the range of all real numbers when the exponential function only has a...

Homework Statement Find the Domain of f f(x)=2+7x (2+7x is in square root) Homework Equations The Attempt at a Solution I'm really not sure. The possible answers i think of seem far to easy. This problem's annoying me because i remember doing it in alg. 2 but it was so long...

Homework Statement I want to integrate a function over an Ellipsoidal domain. \[...

Say we have a function, f(x)=x^3 one would say "f is a function from \mathbb{R} to \mathbb{R}" or f: \mathbb{R}\to\mathbb{R} Then say we have a vector function, \vec{g}(t)=<t^2+1,t> . How would one use the above notation? Would it be \vec{g}: \mathbb{R}\to\mathbb{R}^2 ? And...

Hello everybody! I am trying to construct the FDFD method for 3D structures. I have already constructed the general formulation and specifically I have set the complete matrix form. Due to the fact that the matrices are too sparse, and my system is out of memory, I am trying to set the problem...

In other words, is the domain of a function by definition non-empty? (If I define a function from A to B should I take care to ensure that A is non-empty?)

Prove that the group ring ZpG is not a domain. Homework Statement Let G be a finite group and let p >= 3 be a prime such that p | |G|. Prove that the group ring ZpG is not a domain. Hint: Think about the value of (g − 1)p in ZpG where g in G and where 1 = e in G is the identity element of...

So I created this storage container object for a program I need to write for C++. In applying my way to store data in a single 2dimensional array I came across a weird connection, and after trying to connect the dots I find myself trying to represent what I can only describe as the domain...

Homework Statement I'm looking at integrals about the unit circle and need to show that they equal 0. integral[e^zdz/(z-2)] integral(sinz/zdz) integral[sinhz/(z^2+2z+2)dz] My thoughts on showing these is using series. Is this the right idea? Also I'm looking at a couple of...

If a function f is differentiable at a point x = c of its domain, then must it also be differentiable in some neighborhood of x = c?

Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance... For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain...

Hello, For spring break homework, I'm supposed to prove the Invariance of domain theorem (stating that continuous injective functions from an open set in R^n to R^n are open maps). Does anyone know of any books/sources of any kind which will help? Thanks!

Homework Statement How do you know whether you restrict the domain or range with a horizontal ellipse ? Homework Equations x^2/49 +y^2/10=1 The Attempt at a Solution

1. Let f(x)= 1/x where x is a rational number. What is the domain of f? Give a codomain and image for f that are not equal to each other. I am not sure about my answers, I got: D= (-infinity, 0) U (0, infinity) Image= (o, infinity) Codomain= Set of all reals I don't think this is...

Can you help me with this? I have a function with domain and range in R^2. What conditions it must have so that a point in the boundary of the domain will have its image in the boundary of the range? Thanks.

domain and range of the function help needed.. work shown! Given the function f(x)= (3x+4)/(5-2x) find the domain and range of the inverse function of f(x) work shown: it was proven to be one to one since f(x1)= f(x2) found inverse f(x) to be (5x-4)/(3+2x), i believe this is correct...

define the natural domain and range for f(x,y) = 1/sqrt(x^2-y) I get D= {(x,y)|x^2-y>0} same as saying y can not equal x^2 R= {(x,Y)|f>0} can someone tell me if I've approached this correctly?

Hello, This is the first time I'm using COMSOL on a problem where I have multiple subdomains within the domain. Previously, I have only been using one domain/one set of equations/Two global sets of BC's. I've been having a hard time thinking of a solution to my problem. I have 3...

Does Cramer's rule work in frequency domain? For example, if we have to solve two simeltaneous equations, as in nodel analysis or mesh-current method, can we use Cramer's rule to solve em? Would this be an efficient method?

Homework Statement I have a review in Calc and the question was: f(x) has a domain of [-1 , 5) Find the domain of g(x) = f(2x+3) Homework Equations The Attempt at a Solution I got [-1 , 2)

f(x)= x^(5/3) - 5x^(2/3) Need to find the domain of the above function? The graphing calculator shows x cannot be a negative number, and I don't see why not? Please help!

Homework Statement Dear all , Am new to matalb and am having some couple of problems. i want to convert the following wave form from time to frequency domain . 1.E=ACos(ωt+φ).[0,T] I have made conversion by using integration by parts.Please find the MATLAB attached files...