Domain Definition and 704 Threads

how is euler's formula useful? it must have something to do with converting from the time domain to the phasor domain and back, but i can do that without euler's formula

"Natural Laws" and their domain of validity What is the philosophical justification for extending observed phenomena to "laws of nature". For example, Galileo dropped massive objects and saw that they fall at the same rate, but to then say that all massive objects fall at the same rate requires...

\int _1 ^e \int _{1/e} ^{1/y} f dx dy If asked how to sketch the bounds for that: "x starts at x=1/e and ends at x=1/y 1/e is just a constant so that's a straight line and x=1/y is the exact same line as y=1/x" That's a decent enough engineer's explanation right? (no one in university should...

Prove that the solution of the CP y'=-(x+1)y^2+x y(-1)=1 is globally defined on all of \mathbb{R} How would you go about this? I thought about studying the sign of the right member if the equation. But what would I do next?

Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help. Thanks.

Homework Statement Given two functions f(x)=\frac{x}{x+1} , g(x)=\frac{x+2}{x} (1) find the domain of f and g so D_f all real x , x\neq -1 D_g is all real x , x\neq 0 (2) Find the composite function gf and state its domain and range g o f = 3+ 2/x , then its domain would...

I read a lot of books on the uniqueness theorem of Poisson equation,but all of them are confined to a bounded domain \Omega ,i.e. "Dirichlet boundary condition: \varphi is well defined at all of the boundary surfaces. Neumann boundary condition: \nabla\varphiis well defined at all of the...

hi ,,,, Homework Statement these are the function 1) f(x)=A(x)/B(x) 2) f(x)=√(A(x)) 3) f(x)=√(A(x))/(B(x)) 4) f(x)=(A(x))/√(B(x)) 5) f(x)=√(A(x))/√(B(x)) 6) f(x)=√((A(x))/(B(x))) The Attempt at a Solution the domain are they right 1) { x∈ R : B(x) ≠ 0 } 2)...

Homework Statement Let the function f: [1,infinity)-->R f(x)=\left\{ \begin{array}{rcl} \frac{(\sqrt{x}-1+x\sqrt{x-1}}{\sqrt{x^2-1}} & \mbox{,} & x>1 \\ c, x=1 \end{array}\right. Find the EXACT value of c for which f is continuous on its domain. Homework Equations N/A...

Just wondering how to write the domain of where a function similar to this is continuous: using proper domain notation.

1.Let R be a ring such that Z ⊂ R ⊂ Q. Show that R is a principal ideal domain. We show that Z is a principal ideal domain, so every ideal in Z which is also in R is principal. But I'm not sure how to use that R is contained in Q. 2. Proof that X^4+1 is reducible in Z/pZ [X] for every...

Homework Statement S = { z | |Im(z)| < 5 }, z is a complex number Homework Equations I am trying to generate a mobius transformation w = f(z) such that it will map S onto a unit disc but I keep running into problems and contradictions. I think there is a big mistake in my attempt but I...

I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...

Hi, I'm working on a calculation of flow through a rectangular duct and I'm assuming I'm in the Stokes' flow regime (Re<<1), but I also want to experiment on this system and I was wondering if anyone knows until what Re-number Stokes' flow is still a good approximation (and how good, i.e. in...

Symmetry breaking "domain walls" The only "spontaneously broken symmetry" that I can easily visualize, is cooling down a ferromagnetic material and having the spins randomly choose a direction to align. Since the choice is random, different regions will usually choose different directions...

I was working on the following problem from a textbook. The textbook has no answer. I have included my solution - I am not sure whether it is correct Any ideas and or solutions? (guidance) Question: Suppose that f is any function with domain (-infinity, +infinity) a) Does the function g...

Homework Statement I am trying to find the domain of the following.. R^2 to R^3 of g(x,y) = (x-y,x+y,3*x) R^3 to R of h(x,y,z) = x/(y+z) Homework Equations The Attempt at a Solution I don't know how to start. I know how to find the domain in one dimension but how...

Homework Statement Find the range for the function; fg(x) and state its range where f(x)= e^{2x} + 3 and g(x) = ln(x-1) The Attempt at a Solution Putting g into f I reach; fg(x) = e^{2ln(x-1)}+3 (1) - here is where I have the problem, now, I know that it simplifies down to fg(x)...

Homework Statement Find the domain of the function. h(x) = \sqrt{4 - x} + \sqrt{x^2 - 1} Homework Equations a2 - b2 = (a - b) (a + b) I think that's all... The Attempt at a Solution For starters, I know we can't have a negative number in the radical. I looked at the 2nd radical first and...

Hello. I am watching this video: https://www.youtube.com/watch?v=xIQtnQ9XPbE and he says there: I see that the wave turns into a "normal" sinus in the end, but it's not constant. I think, that even on an unmatched transmission line, the waves should go back and forth, but eventually...

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...

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...

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...