Domain Definition and 704 Threads

Homework Statement If a ball is thrown into the air with a velocity of 40 ft/sec, its height (in feet) after t seconds is given by s(t) = 40t -16t^2. Find the average velocity, vAV (t), of the ball over the time interval (t, 2), for 0 < t < 2. Homework Equations change of x/change of...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Section 1.4: Entry 2: Axioms for the Integers ... In this section Bloch defines the integers as an ordered integral domain that satisfies the Well Ordering Principle ... rather than defining the...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Section 1.4: Entry 2: Axioms for the Integers ... In this section Bloch defines the integers as an ordered integral domain that satisfies the Well Ordering Principle ... rather than defining the...

Nearly every analysis reference I come across defines the derivative for functions on an open interval ##f:(a, b) \rightarrow \mathbb{R}##. I understand that, in constructing the definition of ##f## being differentiable on a point ##c##, we of course want it to first be a point it's domain, so...

Section 3.1 Question 2dFind the domain of the function. Let CR = CUBE ROOT s = CR{3t + 12} Because it is a cube root, I say the domain is ALL REAL NUMBERS.

the graph of sin inverse (sin x) between the domain of ( -pi/2,pi/2) is y = x. but after it crosses that domain of course the expression won't be the same anymore because sin inverse has its principle value as ( - pi/2, pi/2) due to sin x many to one natured function. now the way these...

Specify the domain of each variable. 1. ax + b Here x can be any integer. In that case the domain is R, where R is ALL REAL NUMBERS. 2. ax^(1/3) + b Let x^(1/3) be the cube root of x. Let D = domain x^(1/3) is > or = 0 [x^(1/3)]^3 > or = 0^(1/3) x > or = 0 D = {x| x > or = 0} Is any...

Why must we restrict the domain of certain functions to solve the problem?

Find the domain of the rational function. y = (6x^2 + 11x + 4)/(3x + 4) Solution: Let denominator = 0 and solve for x. 3x + 4 = 0 3x = -4 x = -4/3 This means the domain is any real number except for x = -4/3. When x = -4/3, the denominator becomes 0, which is undefined. Correct?

Just a quick question - Is it true that the domain of ##f'(x)## will always be less than or equal to the domain of the original function, for any function, ##f(x)##?

Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 5b Specify the domain. 4/[(t - 1)•sqrt{t}] Solution: Set (t - 1) = 0 and solve for t. t - 1 = 0 t = 1 For sqrt{t}, the radicand cannot be negative. Domain: t can be any number except 1; t > or = 0. Yes?

Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 3b. Specify the domain. ax^(1/3) + b Solution: x^(1/3) means the cube root of x. Since there is a radical here, I will say the domain is the radicand > or = 0. So, x > or = 0. Yes?

Hi, I have a question about steel, for instance, silicon steel used in magnetic cores. I was wondering about how Iron magnetises: can you align the grains/domains and heat treat it [or anything], so that it responds differently to flux one way then the other direction? For example, say you...

Homework Statement Hello! Seems I have forgotten how to work with such values. Please, help me to find the correct approach to this type of exercises. Homework Equations The task is to find the domain of the function: f(x) = arccsc(e2x) The Attempt at a Solution The answer in the book is [0...

I am trying to implement several filters in Matlab for Fourier domain filtering. They are the cosine, Shepp-Logan, and Hann/Hamming window filters. These filters are defined as multiplying the ramp filter by the cosine function, sinc function, and Hann/Hamming windows respectively. This is how...

Homework Statement Show that ##\mathbb{Z} [\sqrt{d}] = \{a+b \sqrt{d} \ | \ a,b,d \in \mathbb{Z} \}## is an integral domain Homework EquationsThe Attempt at a Solution Do I have to go through all of the axioms to do this? For example, do I have to show that it is an abelian group under...

Homework Statement Let ##R## be an integral domain and ##p_1(x),p_2(x) \in R[x]## with neither equal to ##0##. Show that the degree of ##p_1(x)p_2(x)## is the sum of the degrees of ##p_1(x)## and ##p_2(x)##. Homework EquationsThe Attempt at a Solution Here is my attempt. Let ##p_1(x) = a_n...

When considering the Wave equation subject to initial conditions as follows… …then D'Alembert's solution is given by (where c is wave speed): I'd like to understand physically how this formula allows us to know the value of u (where u is the height of the wave, say) at some point (x0,t0)...

Find the domain. ax^(1/3) + b I understand that a and b are constants here. I also know that x^(1/3) is equivalent to cube root{x}. What I do not understand is why the answer is ALL REAL NUMBERS.

Hello All, I would like to convert a partial diff equation in time domain into frequency domain, however there is a term of the form: Re(∇(E1.E2*) exp(j[ω][/0]t)) where E1 and E2 are the magnitudes of the electric field and [ω][/0] is the angular frequency. Can someone please help me to...

I have these assumptions please correct me if they are wrong:) 1)A particle has mass,electric charge and magnetic moment. 2)Somehow in a atom the net magnetic moment of all the particles including protons and electrons get canceled out and becomes neutral.However for half-filled electron shells...

Homework Statement find domain f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ## Homework EquationsThe Attempt at a Solution [/B] Well, one sees that x ≠5 and then we further investigate the dividend portion where the under-the-root expression ≥ 0 We can graph the parabola, and find the zeroes. Then...

Suppose we have a "particle" which can be at some position x∈N (where N={0,1,2,...}). The probability that the particle is at position x can be written as: P(x) = 1/(2x+1) Now suppose we have two particles p1 and p2.To keep things simple, assume that the individual probability distribution for...

Homework Statement Homework EquationsThe Attempt at a Solution So far I was able to transform each element into the frequency domain: I am just unsure how to work with the dots to find the mesh currents. Can someone explain? Thanks.

Joseph A. Gallian, in his book, "Contemporary Abstract Algebra" (Fifth Edition) defines an irreducible element in a domain as follows ... (he also defines associates and primes but I'm focused on irreducibles) ... I am trying to get a good sense of this definition ... My questions are as...

Joseph A. Gallian, in his book, "Contemporary Abstract Algebra" (Fifth Edition) defines an irreducible element in a domain as follows ... (he also defines associates and primes but I'm focused on irreducibles) ... I am trying to get a good sense of this definition ... My questions are as...

Hi everyone, I've been looking at a problem that seems simple at first, but appears to be deceptively difficult (unless I'm missing something). 1. Homework Statement I've been looking at a problem that involves the diffusion of a scalar quantity, ##q(x)##, on the semi-infinite domain, ##\leq...

Boltzmann's constant appears in many distributions of statistical physics, and I have been left confused whether it is always the same constant with certainty. For example, suppose we define the Boltzmann's constant so that it is the constant that works with certainty for gases, i.e. it gives...

Homework Statement f(x,y) = 1/y^2-x find the domain of f. Given c ∈ R \ {0} find (x, y) ∈ R 2 such that f(x, y) = c. Finally determine the range of f. Homework Equations I know that the domain of the function is anywhere that the function is defined. The Attempt at a Solution in the case of...

I am having difficulty thinking through how a ferromagnetic substance is permanently magnetized. I think I understand that when for example a sample of iron is heated above it curie temperature and then exposed to an external magnetic field , the sample will become permanently magnetized. The...

can anyone help me ? i have a homework and i did't find any answer for it the question is find the Domain , Range , matrix and the digraph for the relation R a ) A = { 1,2,3,4,8 } = B , aRb if and only if a=b b) A = { 1,2,3,4,6 } =B , aRb if and only if a multiple of b

Homework Statement Homework EquationsThe Attempt at a Solution I am extremely confused. Everywhere I go to look on how to convert phasors into time domain I get a different answer. I am trying to convert -j to the time domain. My notes says to find the Im(phasor). I have explained in the...

Hello. Let's have any non-zero complex number z = reiθ (r > 0) and natural log ln applies to z. ln(z) = ln(r) + iθ. In fact, there is an infinite number of values of θ satistying z = reiθ such as θ = Θ + 2πn where n is any integer and Θ is the value of θ satisfying z = reiθ in a domain of -π <...

I'm switching my personal e-mail to an address @ the domain name that I use for my web site, so that in the future I can switch e-mail providers by pointing the address to the new provider instead of having to tell everyone a new address. Of course, this time I still have to tell everyone, but...

1) How many stages are in N numbers for a FFT? I know N=8 has 3 stages and N=4 has 2 stages ? 2) The DFT formula converts a signal from the time domain into the frequency domain. Is this done by comparing x[n] against signals known as sinusoidal basis functions? are e-j2 pi kn/N sinusoidal...

Assuming that a TLP platform is examined and the wave forces acting on the tendons of the mooring lines are presented in RAOs (as a function of wave frequency). Using Jonswap spectra for North sea (i.e peakness factor equal to 3.3) we can obtain Hs (significant wave height); Tp (peak period) and...

Homework Statement Find Amplitude of Steady-state voltage across capacitor Homework EquationsThe Attempt at a Solution I'm at the very last step of changing it back into the time domain to obtain my ampltiude. I was planning on getting it into the form a + bj, then using trigonometry and...

Homework Statement for the domain of ln (x^2 + y^2 ) , it it given in my notes that the ans is x ≠ 0 and y ≠ 0 IMO , it's wrong to give x ≠ 0 and y ≠ 0 , because the meaning of x ≠ 0 and y ≠ 0 is that x and y can't be 0 all the times so just leave the ans (x^2 + y^2 ) > 0 , will do ...

Homework Statement in my notes , it's stated that the domain of ln(x+y) is x+y> 0 ... Can i write it as x ≠ 0 , y ≠ 0 ? Or should i write it as (x,y) ≠ (0,0) ?(x,y) ≠ (0,0) represent x , and y can be 0 at the same time ? Whereas x ≠ 0 , y ≠ 0 only represent x can't be equal to 0 ? for...

Homework Statement the given ans is x ≠ 0 , y ≠ 0 , the ans given is x ≠ 0 , y ≠ 0 . I don't understand the ans , why the author leave the ans like this ? IMO , x can be 0 as long as y not = 0 y also can be 0 , as long as x not = 0 ,by giving the ans in x ≠ 0 , y ≠ 0 , the author just rule out...

Homework Statement Suppose we have f(x,y) = ∑(x/y)^n , n goes from 0 to infinity. What is the domain on the xy plane? Sketch it. 3. Attempt I was thinking to look at the scenario if x/y is less than 1, or bigger than 1. If the ratio is less than 1, then I can use an idea from geometric series...

When working in the complex domain (##z = x + iy##), how does one write the equation of a line? I have attached a problem I was working on (and have the solution), but am curious as to why the definition of a line is given by ##ax + by = c##. Are not ##x## and ##y## also variables that take on...

Hello, I'm sorry for registering to the the boards and immediately posting a new thread. I did use the search function to try and find a similar thread that addresses the issue I'm having but nothing jumped out at me and frankly I'm so green that I wouldn't know what to look for. This is my...

Homework Statement The (computing) task at hand is to take a function f(x) defined at 2N discrete points, and use the Discrete Fourier Transform (DFT) to produce F(u), a plot of the amplitudes of the frequencies required to produce f(x). I have an array for each function holding the value of...

Homework Statement A rectangle has one vertex in quadrant I at the point (x,y) which lies on the graph of y = 2x^2 and another vertex at the point (-x, y) in the second quadrant and the other vertices on the x-axis at (-x, 0) and (x, 0) What is the domain of the area function? y = 2x^2 = w l...

Dear All, Suppose we have a electromagnetic/x-ray pulse with fixed energy with finite line width. I want to know the schematic of a plot how it looks in time- and frequency-domain? I think I understand in time domain: there will a straight vertical line on plotting intensity vs time in x-axis...

I was wondering if our governments hide us some knowledge. Military industry for sure, but What about physics? Is all the knowledge public? I include in my question biology. I am sure that the richest people in this planet are investing right now hundreds or thousands of billions researching...

Homework Statement Suppose f is a function with domain [-2,10] and range [5,10]. Find the domain and range of the following functions. (a) f(2x+4) (b) 2f(x)+4 The Attempt at a Solution [/B] Would I just substitute the in the domain and range values to find the answer?

Hi all, I need some help regarding domain wall geometries, essentially a bubble of some spacetime (say deSiiter or flat) inside another kind, say anti-deSitter. For simplicity it is spherical symmetric situation and we are intent on using Schwarzschild like static coordinates. So now I am used...

I have the expression $$\sqrt{ a ^2 - x^2}$$ using trig substitution (with $x = asin\theta$), I get$$\sqrt{ a ^2 - a^2sin^2\theta}$$ which gets simplified to $ a \sqrt{ cos^2\theta}$ and then $ a cos \theta$ for $$- \frac{\pi}{2} \le 0 \le \frac{\pi}{2} $$ what I don't get is domain of...