Domain Definition and 743 Threads

Homework Statement Here is a picture of the question: Homework Equations The Attempt at a Solution Here it what I did... factored it...so 1 / (x-3)(x+17) domain: (-infinity, -3)(-3,17)(17, +infinity) or rather (-3,17) I know that is not correct. I am really stuck on this one!

What is the domain of f(x)=x^(2/3)? If I take a negative number and square it, the result is positive. For example, (-4)^2 is 16. The cube root is 16 is also a positive number. So I conclude that the domain of this function is "all real numbers". But in Wolfram the answer is "all...

If I am given a function: f(z) = w(x,y) = u(x,y) + iv(x,y) How do I find the domain and range of that function? Are there any good lectures online on this? I know I have to use two planes; One for u and v, and one for x and y. Besides that, I am lost.

I am a bit confused about this matter. While I was studying Calculus I saw an excercise like this: The domain of f(x) [0,2] and the range is [0,1], it also shows its graphic, though it is not important it is something like a parabola, its maximum point is (1,1) and its intersection points are...

Hello, I know the value of a field variable in a 3d mapped finite element mesh. Can anyone suggest an effective method/methods to find its gradient throughout the mesh.

Hello, I have a simple question that has bothered me forever.When I am given a rational function, say, f(x) = (x2+x-6)/(x+3)say I want to look at the domain of this function. Well the first thing that catches my eye is the fact that if I plug in x=-3, the denominator will be 0, which would be...

Hello All, I am Acharya, from INDIA . I need some career guidance. I have done my B.Tech in Electronics and Communication Engineering, and my Master's in Nanoelectronics, duirng my Master's i have done my project on Lattice dynamics, I want to do Doctorate in Density functional theory...

Homework Statement Hello! Could someone explain some things presented in this example: http://i.imgur.com/wVOxf.png My friend, and I haven't been able to crack it. I get all the x-conditions right, but can't put the whole thing together into a domain. Here it's presented that xe[-2,3] due to...

f(x) = x - 3, g(x) = +\sqrt{x} Q. Find gf(x) and a suitable domain and the corresponding range. so gf(x) = \sqrt{x-3}, f(x) is first and the domain for f(x) is x belongs to ℝ, so the domain for g(x) will be x belongs to ℝ, so this function doesn't work? the answer is the domain is x>=3...

Homework Statement Consider the function f(x) = sin (x) in the interval x ∈ (p/4, 7p/4). The number and location(s) of the local minima of this function are? Homework Equations The Attempt at a Solution I have managed to get one of the minimas (i.e. 3p/2), however i am unsure about...

Preface: I can't understand a solution provided in a textbook. Please help me to understand. Homework Statement Define: f : D_f \rightarrow \mathbb{R} such that f(x) = \sqrt{x+2} and Domain(f):=D_f = \{x \in \mathbb{R} : x \geq -2\} Find the range of f(x). 2. The textbook's solution...

Homework Statement Find the domain and range of the function: F(x) = \frac{x}{lxl} Homework Equations ? The Attempt at a Solution domain is all x such that x ≠0 range: do i have to make this into a piecewise function, if so, how?

How will the graph of a sine wave (plotted against time axis) of a particular frequency look like if the same is plotted against frequency?

Homework Statement Eliminate the parameter to find the Cartesian equation of the curve. Problem #1: x = sin t, y = csc t, 0 < t < ∏ / 2 Problem #2: x = sin θ, y = cos 2θ Homework Equations What's shown above is what's listed in the book. However, the authors felt compelled to...

It's a pretty basic equation: x = x^u, solve for u. ln x = u ln x ln x / ln x = u u = 1 However, this solution only applies for x > 0. Is there any way we could solve this equation for all values of x?

Homework Statement Let R be an integral domain. Say a prime p \in R is small if a\in\bigcap\limits _{n=1}^{\infty}\left\langle p^{n}\right\rangle = \left\langle 0\right\rangle Show that if p is a small prime and D = R \setminus \left\langle p\right\rangle then R_D is a principal ideal...

Homework Statement I need to compute the following using the Jacobian: \int\int_D \frac{x-y}{x+y} dxdy Where D = \left\{(x,y):x\geq 0, y\geq 0, x+y \leq 1\right\} Homework Equations The Attempt at a Solution I've made the transformation: s=x+y \qquad t = x-y My problem is finding the...

Hi, I am trying to understand the impact of cut off frequency on the gain and trying to relate it in time domain but unable to do so. For e.g., I have built a single pole RC filter wherein R and C values are chosen to match the cut off frequency of 1K (R = 10KΩ/C = 16nF). The input is a square...

Homework Statement See attached file. Homework Equations The Attempt at a Solution I've only been able to do part (a) of this question. I ended up with: tanz= i ({\frac{1-e^{(2iz)}}{1+e^{(2iz)}}}) I'm not sure how to approach the next two parts. If anyone could give me any...

Homework Statement Consider a lamina (two dimensional plate) with edges given by the lines y = sqrt(x) and y = -x + 2x^(2), for which the density is given by P(x; y) = x. (a) Define the domain of the lamina as the union of a Type 1 region and a Type 2 regions. b) Calculate the mass. Just...

Homework Statement f(x,y)=2x3-2y3-3x2 K={(x,y)\inℝ2:x2+y2≤5,y≤0} Find the maximum and minum of f(x,y) within K. Homework Equations ∇f(x,y)=(6x2-6x,-6y) Hess(f)=diag(12x-6,-6) (relevant?) The Attempt at a Solution What I've done so far was calculate the pair(s) (x,y)...

I am trying to show that $\mathbb{Z}[\sqrt{-3}]$ is not a euclidean domain, now I know that in every euclidean domain we have that an element is prime iff it is irreducible so I need to find an irreducible element of $\mathbb{Z}[\sqrt{-3}]$ that is not prime, I can't seem to think of one...

I keep reading through the course textbook but no matter how many times I read it I just can't see the understanding of it? There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student...

Just for clarification, I was wondering if someone could clarify what the difference between a magnetic moment and magnetic domain is. My understanding is a magnetic moment is when the atom aligns it's subatomic particles relative to the magnetic field, and that a magnetic domain is groups of...

Hello, I need to sketch the frequency domain for the following AM waveform showing total bandwidth and frequency. 8sin(2pi500kt - 4cos(2pi530kt) + 4cos(2pi(470kt) I have attached an attempt I have made. Does anyone know if I have this correct or not ? Thanks kindly for any input.

I need a physical explanation of s domain..Is s-domain a higher dimensional plane..?

I'm curious if anyone knows why my calculator would return "Domain Error" when calculating (-i)^4 on my TI-36X Pro? ((-i)^2)^2 works just fine on the machine, and (-i)^4 works just fine on my TI-83 Plus. Any ideas?

1. Evaluate the integral ∫VxdV inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1 Answer given: 1/8 - √2/16 (which is NOT what I got.. ) 2. The attempt at a solution Ok, it's a triple integral, I know this. ∫dx runs from 0 to 1 ∫dy...

gcd(a,b) unique in Euclidean domain?? Homework Statement In Hungerford's Algebra on page 142, the problem 13 describes Euclidean algorithm on a Euclidean domain R to find THE greatest common divisor of a,b in R. My question is that does this THE mean THE UNIUQE? I've heard from my lecturer in...

√Homework Statement √(log1/5(1/Sin5x)) Log to the base 1/5*(1/Sin5x) FIND THE DOMAIN I have an answer to this solution, I Just need some help with understanding it :(... and also could someone tell me if info is missing. f(x) = √(log1/5(1/Sin5x)) Restrictions: 1/sin5x ǂ...

Hi, I am wondering how to express the domain of a two-variable function f(x,y) as below. For any given y, f(x,y) is defined on [0, g(y)); for any given x, f(x,y) is defined on [0, h(x)). Then how should I specify the domain for the function f(x,y)? To be more specific, f(x,y)=x+y, and...

Homework Statement Two waves on a string are given by the following functions: Y1 (x,t) = 4cos(20t-x) Y2 (x,t) = -4cos(20t+x) where x is in centimeters. The waves are said to interfere constructively when their superposition |Ys| = |Y1 + Y2| is a maximum and they interfere destructively when...

for example if f(x) = \frac{x^{2} - 1}{x+1} they by factoring: f(x) = \frac{x^{2} - 1}{x+1} = \frac{(x + 1)(x - 1)}{x+1} = x - 1 thus the simplified version is x - 1 let's say g(x) = simplified f(x) g(x) = x - 1 meaning g(x) = f(x) but g(-1) ≠ f(-1) am I missing something?

I know that, for k an integer, the rose polar curve expressed by r=r(θ)= cos(kθ) has a period of π if k is odd and 2π if k is even (usually expressed as saying that there are k distinct petals if k is odd, and 2k petals if k is even). However, I have yet to pin down the reason for this...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...

Homework Statement Given the function, state the domain and range. I just want to make sure my notation is correct? More specifically, the I am f, can you have the independent variable in there? Here's my answer: http://tinypic.com/r/2nlda2q/5 Homework Equations The...

1. I was asked to roughly sketch a graph given the information seen, in the below picture, to the right of the graph. 2. My actual graph is done by hand and the lines are not as straight, but the general shape is the same. Does it look approximately right? The areas I am worried...

Homework Statement State the domain and range of the function that models each half of the roof (triangle) Homework Equations Y= -0.7x+1.9 (left half) Y= 0.7x+1.9 (right half) The Attempt at a Solution Why is the answer: Left half: domain: −2.7≤x≤0 range: 0≤y≤1.9 Right...

As we know , the average value of a function over is : i wanted to calculate the average value of a function over its entire domain ( e.g ) firstly, i divided the interval into 2 intervals & and calculated the F_avg for each ,,, is my way correct ? thanks !

In the first volume of Differential Geometry, Ch. 1, Spivak states that if U \subset \mathbb{R}^n is homeomorphic to \mathbb{R}^n, then U is open. This seems obvious: \mathbb{R}^n is open in \mathbb{R}^n, so its pre-image under a homeomorphism f:U \rightarrow \mathbb{R}^n is open. The pre-image...

Did you know first internet domain was registered exactly 27 years ago, on March 15th? http://symbolics.com/

[b]1. what is the domain of the function k(y)=1/(2y+1)? Express your answer in interval notation [b]2. [b]3. I find that 0.5 is a possibility in this function, but since i have not done functions at school, i do not really know much more of this question.

Hi everyone, I'm currently looking to solve an equation of the general form: \sqrt{x^2-y^2}+\sqrt{\epsilon x^2-y^2} = \beta. I'm interested in solving this equation for x assuming y>0, \epsilon>1 and \beta \in \mathbb{C}. By squaring the equation twice I can find four potential solutions of...

Homework Statement so I am supposed to find the domain of the function, the range, describe its level curves, find the boundary of the functions domain, determine if the boundary is an open region, a closed region, or neither, and decide it the domain is bounded or unbounded...

Homework Statement x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2) find the domain of continuity Homework Equations none The Attempt at a Solution I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf) but the professor then asked...

Homework Statement I'm trying to write a proof ot demonstrate that every finite domain contains an identity element.Homework Equations The Attempt at a Solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider...

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

Okay i need to find expressions for v1 and v2 and I am using nodal analysis: these are not the final the equations just initial equations by first look I am good finding expression for v1, (2/s)-(v1/1)-((v1-v2)/(2/s)) = 0 Where i am stuck is with the current source and 2 ohm res...

Is this claim true? Assume that X,Y are topological spaces, and that all closed subsets of X are compact. Then all continuous bijections f:X\to Y are homeomorphisms. It looks true on my notebook, but I don't have a reference, and I don't trust my skills. Just checking.

I'm asked to find the domain of 1/[e^(x+y)-3] Which means I'm solving for e^(x+y)>=3 But how would I go about solving this?