Domain Definition and 704 Threads

Homework Statement I need to find the domain of absolute convergence of the following series: ^{\infty}_{1}\sum(z+3)^{2n}/(2n)! Homework Equations Ratio test? The Attempt at a Solution I'm not really sure how to handle the complex variable z within the series. I attempted to use the...

Homework Statement Suppose that the function f is defined on an interval by the formula f(x) = \sqrt{tan^{2}x - 1}. If f is continuous, which of the following intervals could be its domain? (A) (\frac{3\pi}{4},\pi) (B) ( \frac{\pi}{4},\frac{\pi}{2} ) (C) ( \frac{\pi}{4},\frac{3\pi}{4}...

Homework Statement Find the domain and range: { x+2, x\leq0 f(x) ={x3, |x|<1 {-x+3, x\geq1 Homework Equations domain = possible inputs range = possible outputs The Attempt at a Solution domain of f(x) = (-\alpha, -1] \cup (-1, 1) \cup [1, \alpha)...

I have a question about domain. Let's say we have a function in the form of y=(C/X)^0.5 Let's say for a particular case C = 0. Is the domain of the function x cannot equal 0? Or is it all real?

f(x) = -√(t(1-t)) Domain: 0≤t≥1 (from Null Factor law) Range: 0≤t However, the range was wrong. The answers said that it was -0.5≤t≥0. I have no idea where the -0.5 came from. I substituted the domain values in but i didn't work. It just came out with zero. Can anyone suggest any ideas...

Show that if R is an integral domain with characteristic p>0, then for all a,b in R, we must have (a+b)^p=a^p+b^p. Show by induction that we must also have (a+b)^p^n=a^p^n+b^p^n for all positive integers n. R is an integral domain, so ab=0 implies a=0 or b=0. The smallest positive integer...

Consider the mapping f: X\rightarrowY where f(x)=y=\sqrt{1-x^2} consider the co-domain Y , we can define the mapping over [-1,1] \rightarrow \mathbb R , ( in this case the mapping won't be onto) and in case we define the mapping over [-1,1] \rightarrow [0,1] (in this case mapping is onto) (is...

Greetings to all. :smile: I have 2 simple questions, one is simply a confirming the answer query, and the other is domain related (like topic title says). 1) In this question, we are asked to show that a2+b2 is constant for all values of \theta. We have a and b as...

Homework Statement My domain i numbers of form 4k+1. n divides m is this domain if n=mk for some k in the domain. A number is prime in this domain if its only divisors are 1 and itself. My problem is to find a number in the domain with multiple prime factorizations. Homework Equations...

Boundary conditions & time domain electromagnetic waves: does classical model fit? Consider two propagating media: a lossy dielectric medium and a lossless dielectric medium. Thus, the interface that separates them has two tangential components of electric field, one for each medium. One of...

Homework Statement Let R be a ring with no zero divisors such that for any r,s\in R, there exist a,b \in R such that ar+bs=0. Prove: R=K \oplus L implies K=0 or L=0. Homework Equations Definition of direct sum of modules, integral domain... The Attempt at a Solution I didn't know...

Homework Statement I don't have a real question, i was looking for where i could find info on the domain of influence, regarding pdes Homework Equations The Attempt at a Solution

Homework Statement determine the char. curve and gen. sol. for x^{3} \frac{\partial{u}}{\partial{x}} - \frac{\partial{u}}{\partial{y}} = 0 Homework Equations find sol and domain of influence when u(x,0) = \frac{1}{1+x^2} show sol is not defined...

hello, i am new here and this is my first post so please bear with me for any mistakes or so.. now my question is about time domain analysis and frequency domain analysis . why should one convert from time domain into frequency domain by using Fourier transform ? and what are...

Homework Statement Let p be a prime number, and let D = {m/n| m,n are integers such that p does not divide n} Verify that D is an integral domain and find Q(D) Homework Equations i am unsure where to use the fact that a prime number divides n in this proof. I know how to check that D is an...

Homework Statement In exercises 39-46, f refers to the function with domain [0,2] and range [0,1], whose graph is shown in Figure P.55 (how do I draw and paste graphs? the graph looks like an upside down curve with a maximum height or range of (1,1) and a width or domain of (0,2)). Sketch...

let a function f: A -> R^m where A is a subset of R^n. if a is an accumulation point of the domain of f, the set A, then f(A) is an accumulation point of the set R^m. i'm not sure if this statement is true or not but if it is, how would I prove this result? i was thinking of using the fact...

Homework Statement Let R be an integral domain with identity element 1. Show that there at most two elements "a" in R such that a^2=1 Homework Equations The Attempt at a Solution Being an integral domain implies that if ab=0, then a=0 or b=0. a^2=1 implies a=1. Then (a)(a) =...

I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...

Homework Statement F(x) \ = \ \int\limits_{1}^{x^2}{\frac{10}{2+t^3}} \ dt Where {0}\leq{t}\leq{4}. Find the domain of F. Homework Equations N/A The Attempt at a Solution I'm not quite sure how to tackle this problem. It doesn't seem as though the domain of t has much at all to do with...

Domain of f(x,g(x)), and partial derivatives Watching http://www.khanacademy.org/video/exact-equations-intuition-1--proofy?playlist=Differential%20Equations Khan Academy video on exact equations, I got to wondering: if x is a real number, what is the domain of a function defined by f(x,g(x))...

Hi everyone! I started studying differential equations, but I still didn't understand why the domain of the solutions must be defined in an interval. For example the solution of the following initial value problem: \frac{dy}{dt} + \frac{1}{t}y=0,y(1)=1 is given by y(t)=1/t that has it's...

how would wavefrom change change in time domain, frequency domain and its rms value if a dc level of 1 volt was added.

I have read a lot of paper about fatigue damage, in some fields it is particularly used the time domain approach while in others the frequency domain approach, but I haven't understood when it is better to use frequency approach respect time domain approach. May you help me to understand better...

Question: Show that if R is an integral domain then R^x=R[x]^x(or that the units in R[x] are precisely the units in R, but viewed as constant polynomials).

Homework Statement Graph x^(1/3) +x^(4/3) Homework Equations Limits, derivatives, etc. The Attempt at a Solution Hi guys, I was attempting this problem and then verifying it using a function grapher online. I noticed that all of the function graphers do not plot the function...

Homework Statement I know that this prob isn't calc, but I'm learning it in calc class now so i thought it would go here :) Anyways, these 3 functions y=1/(x2 y=(x+4)-2 y=1/(x2-x-2) The Attempt at a Solution for this, y=1/(x2 the domain is (-infinity,0)U(0,infinity)...

Homework Statement Prove that R is a PID (principal ideal domain) when R is a ring such that Z \subset R \subset Q (Z=integers, Q=rationals) Homework Equations The Attempt at a Solution So I'm not really sure how to start this problem. I know that a principal ideal domain is an...

hi ... i want to ask about domain theory of ferromagnetism... first of all , According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions, so their magnetic fields will oppose one another and cancel out. how does this happen? after this ...

The Question is: What is the Domain of the function f(x)= log_{5}(log_{5}(x + 2) My answer is that the Domain is (-2, \infty). However the it is said that the right answer is (-1, \infty) and I am not convinced so can anyone give me an explanation?

Hi, I ran into conflicting definitions of integral domain. Herstein defines a ring where existence of unity for multiplication is NOT assumed. His definition of integral domain is: "A commutative ring R is an integral domain if ab=0 in R implies a=0 or b=0" I looked in 3 other books and...

Homework Statement let f(x) = sqrt(1-sin(x)) Homework Equations What is the domain of f? What is the domain of f'(x)? The Attempt at a Solution I understand that the domain of f is all real numbers not including every increment of 90 degrees, but I am not sure how to state that...

Hi together ... I encountered the following statement: Operator A is self adjoint on D(A) then A(t) \equiv \exp(iHt) A \exp(-iHt) is self adjoint on D(A(t)) \equiv \exp(-iHt) D(A). H is self adjoint, so that exp(...) is a unitary transformation. But why does the domain transform this way...

messing around with a function changes it's domain?? consider a function f(x)= \sqrt[3]{2x^2-x^3} if i take x^3 common from inside the cube root the function becomes f(x)= x*\sqrt[3]{2/x-1} the domain of the orginal function includes all real numbers, but the domain of the "new" function...

1) Find a continuous function f: (0,1)->R with f[(0,1)]=R I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions? 2) Find a continuous function f: (0,1)->R with f[(0,1)]=[0,1] I couldn't think of any function that I know. Any suggestions? 3) Find a...

I'm trying to figure out what faraday's law is in terms of frequency rather than time. I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.

Homework Statement Prove that if we have two commutative rings R and S and form the product R X S, then R X S cannot be an integral domain. The Attempt at a Solution We have that an integral domain is a commutative ring with 1 not= 0 and with non-zero zero-divisors. ==> (1,0)X(0,1)...

Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spatial dimension...

Homework Statement Suppose R is an integral domain. Suppose c in R has c^2 = 1. Prove that b must equal either 1 or -1. Also, in Z/12Z, find an element b not equal to -1 or 1, with b^2 = 1 The Attempt at a Solution So for the first part, I'm guessing it would be a good idea to factor...

Homework Statement Find the domain and the range f(x,y)=2x2+3x2+1 Homework Equations non The Attempt at a Solution ... i said that x,y are all real #'s and f(x,y)>=1 or z>=1 is there anything wrong with what i has attempted at? if do could you explain... thanks in advance

can anyone explain that domain or give me any reference about it??

Hey guys, I am totally lost in the idea why we have to change function in time domain to frequency domain to ease with our calculations. Let me break my question into serveral smaller ones. 1)What is the physical implication of transferring a signal to frequency domain? (I know that in...

Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean Thank You

I was thinking how do I differentiate the domain of functions... Suppose I have a function: f(x) = \left\{\begin{matrix} x^2 -1, \;\; |x| \leq 1\\ 1 - x^2, \;\; |x| > 1 \end{matrix}\right. And I need to derive it: f'(x) = \left\{\begin{matrix} 2x, \;\; |x| \leq 1\\ -2x...

Homework Statement Given f:A→B and g:B→C, let h=g(f(a)) If h is injective, then g is injective. Give a counter example. Homework Equations Injection: Let f:A→B For all f(x1)=f(x2) implies x1=x2 The Attempt at a Solution f(a)=\sqrt{a} from [0, infinity]→[0,infinity]...

So I'm skipping pre-cal with full intentions of picking up on AP Calc. Our summer course work is taken from a book called preparing for calculus. After giving me some who-dad that I knew already everything changed in an instant. There's a little gap that isn't quiet filled. A function is...

Hello! I'm not quite sure where to put this. I'm programming, but my question should be strictly mathematical. However, just for your information, I'm programming with Mathematica. I have a function that will give me points. If I give it inputs, I can get a value out of it. I can take a...

Homework Statement Let f(x)=e^(-x)-x ,, x belongs to R Find the domain of f inverse Homework Equations Domain of f inverse = range of f The Attempt at a Solution we have : -inf < x < inf -inf < -x < inf ... (1) 0 < e^(-x) < inf ... (2) By adding (1) and (2) ...

In algebra/trig. what kinds of problems have a domain and a range ? Is this true for anything that can be graphed? Because a lot of the time after you finish a problem in precalc. it then asks for the domain or range, so the question becomes, in mathematics, is it possible to find the domain...

If the domain of a function is countable, then is its range also countable? also if A is countable and B is countable is A(cartersian product)B countable?