Functions Definition and 1000 Threads

Homework Statement This problem concerns the surface determined by the graph of the equation ##x^2 + xy -xz = 2## a) Find a function ##F(x,y,z)## of three variables so that this surface may be considered to be a level set of F. b) Find a function ##f(x,y)## of two variables so that this...

Hi all, I am working on the following integral ## \int_0^{2\pi}\frac{1+\cos[\alpha x]}{1+\sin x}dx ## where ##\alpha## is odd integer. Unless I set the ##\alpha## to a number then I can find the integral with mathematica easily. For general case with symbolic ##\alpha##, I cannot find the...

Everyone "knows" that \lim_{x\rightarrow ∞}\frac{2^x}{x^2} = ∞. We "know" this because 2x grows faster than x2. I use quotes because this is just what we're told in basic calculus classes. But what about a theorem for this? I've searched through google, looked through various university homework...

My undergrad probability theory course just got to random variables and distribution functions. Up until this point, the material was very straightforward and I could understand what was being done, but I feel that I am just not seeing the jump between probability with sets and probability with...

Note from mentor: this thread was originally posted in a non-homework forum, therefore it lacks the homework template. I was wondering if the electric charge density ##\rho({\bf{r}})## of a point charge ##q## at position ##{\bf{r}}_{0}## is given by...

Homework Statement Let ##C## be the space of continuous real functions on ##[0,\pi]##. With any function ##f\in C##, associate another function ##g=T(f)## defined by $$g=T(f)\equiv \int_0^\pi \cos(t-\tau) f(\tau) \, d \tau$$ a) Show ##T## is a linear transformation from ##C## to ##C##. b)What...

Homework Statement Given r(t)=\left< \frac { sint }{ t } ,\frac { { e }^{ 2t }-1 }{ t } ,{ t }^{ 2 }ln(t) \right> Re-define r(t) to make it right continuous at t=0 Homework EquationsThe Attempt at a Solution This is probably the simplest problem ever, but I don't even know what it's asking...

Homework Statement Show that sin 600° . cos 330° + cos 120° . sin 150° = - 1 Homework Equations I know that sinΘ = opposite/hypotenuse and cosΘ = adjacent/hypotenuse. The Attempt at a Solution I am equipped with knowledge about what sinΘ and cosΘ is from right angled triangle. I stand in...

Homework Statement Is there a physical difference between the following wave functions? If yes, why? If no, why not? \Psi(x,0) =5e^{-ax^2} \Psi(x,0) =\frac{1+i}{\sqrt{3}}e^{-ax^2} \Psi(x,0) =e^{i\pi/7}e^{-ax^2} Homework Equations - The Attempt at a Solution They only differ in the...

This is not a homework question but a general doubt. Suppose we have a function y = pcosx, where 'p' is an arbitrary constant. So my question is how will the graph of this function change with different values of 'p'? This doubt can also be extended for other functions like y = pex, y = p...

Homework Statement Determine all primitive functions for the function: 2x(x^2+3)^4 2. The attempt at a solution When i expanded i got the primitive to be: 2(x^9/9)+3x^8+18x^6+54x^4+81x^2But this was wrong. I am not sure I have understood the question. Help?

What's the difference between f(x)=3 and f(x)=3x^0 ? and why Limit of the second function when x\rightarrow0 exists ? and is the second function continuous at x=0 ?

Hello! (Wave) I want to show that the domain of any partially defined recursive function is equal to the range of some ( totally defined ) recursive function. I haven't understood which is the difference between a partially defined recursive function and a totally defined recursive function...

So I have to either prove that these functions are 1 - 1 or show a counter example to prove they are not. I believe that I have proven that these functions are 1 - 1, but I am not 100% sure: For each of the following functions, either prove that the function is 1 – 1 or find a counterexample...

A tad embarrassed to ask, but I've been going in circles for a while! Maybe i'll rubber duck myself out of it. If $$f(t) = f(t+T)$$ then we can find the Fourier transform of $$f(t)$$ through a sequence of delta functions located at the harmonics of the fundamental frequency modulated by the...

Homework Statement Let f(x) = 1−3x−2x^2 , x ∈ [−2, −1]. Use the Horizontal Line Test to show that f is 1–1 (on its given domain), and find the range R of f. Then find an expression for the inverse function f −1 : R → [−2, −1]. The Attempt at a Solution I have already done the horizontal line...

In QFT, the commutation relation for the field operator \hat{\phi} and conjugate momentum is [\phi(x,t),\pi(y,t)] = i\delta(x-y) Maybe this is obvious, but what would the commutator of \phi or \pi and, say, e^{i k\cdot x} be?

Hi, Is the Dyson's equation basis independent (for instance, I construct the basis set where the elements are atomic orbitals and those orbitals are non-orthogonal) ? What is the unperturbed retarded Green's function for one-particle case in matrix notation if the basis functions are not...

Hi everybody! I'm preparing an exam of "Analysis II" (that's how the subject's called in German), and I have trouble understanding how to find the limit of a multivariable function, especially when it comes to proving the uniform convergence. Here is an example given in the script of my teacher...

Homework Statement Homework Equations none The Attempt at a Solution -amplitude is 3 -period is 180° -right 60° -down 1 Rough sketch of graph: I would like to know if the graph looks right, is there any improvements to be made? Thanks :)

Homework Statement Homework Equations 3. The Attempt at a Solution a) The height of the high tide is 4.5 m b) The height of the low tide is 0.25 m c) Period = 12.5 hours k= 360/12.5 = 28.8 amplitude = 2.125 m vertical shift = 2.375 m phase shift = it doesn't look like there is any...

Homework Statement I want to prove this relation ##J_{n-1}(x) + J_{n+1}(x)=\frac{2n}{x}J_{n}(x))## from the generating function. The same question was asked in this page with solution. http://www.edaboard.com/thread47250.html My problem is the part with comparing the coefficient. I don't...

Homework Statement Let C=cosx. Write sec(2x)csc(x)sin(2x) as a function of C. The Attempt at a Solution Am I on the right track 1/cos(2x) * 1/sin(x) * 2sin(x)cos(x) 1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x) What would i do from here?

Homework Statement Homework Equations The Attempt at a Solution a) Here is a sketch of the graph. The lowest point on the Ferries Wheel is 2.5 m and the highest point is 2.5 m + 50.5 m = 53 m. It completes a full cycle every 120 seconds and starts at the lowest point. b) The highest...

I'd like to expand a 3D scalar function I'm working with, ##f(r,\theta,\phi)##, in an orthogonal spherical 3D basis set. For the angular component I intend to use spherical harmonics, but what should I do for the radial direction? Close to zero, ##f(r)\propto r##, and above a fuzzy threshold...

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?

Hello every one . A relation ( is a subset of the cartesian product between Xand Y) in math between two sets has spatial types 1-left unique ( injective) 2- right unique ( functional ) 3- left total 4- right total (surjective) May question is 1- a function ( map...

Homework Statement explained on document attached Homework Equations Energy on a spring and work done by friction The Attempt at a Solution Included on document https://docs.google.com/document/d/1FNrmIkkWzyZJNsbGbq_DYMyMZbpyMcAYKYk9iTbdR-4/edit?usp=sharing

Homework Statement I am unsure if the first statement below is true. Homework Equations \frac{\partial \psi^*}{\partial x} \frac{\partial^2 \psi}{\partial x^2}=\frac{\partial^2 \psi}{\partial x^2}\frac{\partial \psi^*}{\partial x} Assuming this was true, I showed that \int \frac{\partial...

I am confused about the procedure for finding the transition functions given an atlas. I understand the theory; it's applying it to real life examples where I have my problem. So for example, take S1 (the circle). I want to use 2 charts given by: U1 = {α: 0 < α < 2π} φ1 = (cos α, sin α) U2...

I am working my way through elementary topology, and I have thought up a theorem that I am having trouble proving so any help would be greatly appreciated. ---------------------- Theorem: Let A ⊂ ℝn and B ⊂ ℝm and let f: A → B be continuous and surjective. If A is bounded then B is bounded...

The problem $$ \lim_{x \rightarrow \infty} \frac{(\ln x)^{300}}{x} $$ The attempt ## \lim_{x \rightarrow \infty} (\ln x)^{300} = \infty## since ## \lim_{x \rightarrow \infty} f(x) = A## and ## \lim_{x \rightarrow \infty} g(x) = \infty ## thus ## \lim_{x \rightarrow \infty}f(g(x)) = A ##. ##...

Hi All Probably a very basic question. What are the units of the constants in transfer functions? It we take a look at the transfer function of a second order system we then have: H(s) = ω02/(s2+2ζω0s+ω02) ω0 is the natural resonance frequency and has a unit of rad/sec. ζ is the damping...

I'm a programmer looking for a way to create polynomial equations from a list of x intercepts and local maxima. For the sake of discussion we can begin with a function of degree 4. The scale and position of the curve is unimportant so for simplicity's sake the curve can always have x intercepts...

what is the difference between trigonometric identities , equations and functions ...? is it possible to apply some numerical method on a trigonometric function ?? i was looking for an example where numerical methods could be applied on a trigonometric function ... i am not sure what you...

Homework Statement Homework Equations none The Attempt at a Solution a) It is a periodic relationship because the number of hours of daylight repeats each year? OR It is a periodic relationship because the number of hours of daylight is based on the rotation of the earth, which is also...

So I have two sets, call it ##A## and ##B##. I also have a function ##f:A\rightarrow B##. By themselves, it does not matter (or at the very least make sense) to think of ##A## and ##B## as, say, groups (I'm not really thinking exclusively about groups, just as an example). For that matter, it...

Here are my Fortran codes: program test implicitnone integer*4 nxProjPad, cf, numViews, cc, index, indRad, iv, i, INDEX1, d, n real*4 v4, v5, RSS, S1, F1, gMDL real*4, dimension(:), allocatable :: array, sum, cumsum, transpose, log, SS1, SSs nxProjPad=185 numViews=180...

lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...

Hi Physics Forums Is there a specific technique to measure how smooth a discrete function is? By smooth I mean that if you change the input by a minimum amount then you know that the objective function result will not have a big jump. For example The Closest String Problem is completely...

hi all can you browse over this please, to see if I've got this correct as I just want to make sure I am getting it. for the following functions of time,find the amplitude,period ,angular frequency and phase (im assuming it means phase angle there ?) y=3cos (4t+$\frac{\pi}{2}$) amplitude =3...

So I am currently learning some regression techniques for my research and have been reading a text that describes linear regression in terms of basis functions. I got linear basis functions down and no exactly how to get there because I saw this a lot in my undergrad basically, in matrix...

Evaluate $$\left\lfloor{\tan^4 \frac{3\pi}{7}+\tan^4 \frac{2\pi}{7}+2\left(\tan^2 \frac{3\pi}{7}+\tan^2 \frac{2\pi}{7}\right)}\right\rfloor$$. Hi MHB, I don't know how to solve the above problem, as I have exhausted all possible methods that I could think of, and I firmly believe there got to...

Homework Statement In 2003 the city of spring field had a population of 250000 the population is expected to double by 2025, how many people in 2015? Homework EquationsThe Attempt at a Solution A=Pb^t The initial is 250000 and b is 2 because it doubles however I am unsure of what the exponent...

Hi, I have a a Fourier transformed variable \hat{\eta}(k) defined as the following: \hat{\eta}(k)=\frac{e^{-k^{2}}\tanh k}{kU^{2}+(-B+\Omega U+E_{b}|k|-k^{2})\tanh k} The parameters U,B,\Omega,E_{b} have all been defined previously. I have naively tried the following: \eta...

Homework Statement The problem is posted below in the picture. I looked at c and d and can do those. I am unsure about a and b. Homework EquationsThe Attempt at a Solution I looked at graphing the problems, but I think it is a wrong approach.

I am having a hard problem with working on this proof.

I have been working on this exercise 5 and kind of stuck how to start the problems. I would think to start with a graph, but I feel this is wrong. I am just stuck on a and b.

Homework Statement Calculate the convolution of ##sinc(at)## and ##sinc(bt),## where ##a## and ##b## are positive real numbers and ##a>b.## Homework Equations Convolution integral The Attempt at a Solution The fact that ##a>b## tells us that the graph of ##sinc(at)## is ##a-b## times more...

at what value of k should the following integral function peak when plotted against k? I_{\ell}(k,k_{i}) \propto k_{i}\int^{\infty}_{0}yj_{\ell}(k_{i}y)dy\int^{y}_{0}\frac{y-x}{x}j_{\ell}(kx)\frac{dx}{k^{2}} This doesn't look like any orthogonality relationship that I know, it's a 2D...