Functions Definition and 1000 Threads

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 be...

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...

Hi guys. New here. I'm reading philosophy, and this philosopher uses some mathematics which I am having trouble understanding. I am interested in both an understanding of what the signs mean (in themselves and in this context, please), and why someone regularly chooses to use these functions...

In our complex variables course we were told that an analytic function of an analytic function is itself analytic. i.e. For ##h(z)=g(f(z))## ##h(z)## is analytic. I was wondering is this is just a fact, or if it is possible to prove this statement. I did some googling and the best response I...

I noticed the graphs of ##y=\cos^{-1}x## and ##y=\cosh^{-1}x## are similar in the sense that the real part of one is the imaginary part of the other. This is true except when ##x<-1## where the imaginary part of ##y=\cos^{-1}x## is negative but the real part of ##y=\cosh^{-1}x## is positive. I...

Homework Statement δ(z*-z0*)δ(z+z0)=? δ(z*+z0*)δ(z-z0)=? where 'z' is a complex variable 'z0' is a complex number Formula is just enough, derivation is not needed.

Homework Statement What is the product of two Dirac delta functions δ(Real(z-c))δ(Img(z-c))=? 'z' and 'c' are complex numbers. This is not a problem, But I just need to use this formula in a derivation that I am currently doing. I just want the product of these two Dirac delta functions as a...

Homework Statement Homework EquationsThe Attempt at a Solution So far I have a solution for a) as For b) I formulate the equation as and so far for c) I have My main idea at the moment is that as the Lagrangian was not time dependent, the Hamiltonian will not be. Following on maybe...

Homework Statement We are required to find the no. of ordered pairs ##(x,y)## satisfying the equation ##13+12[tan^{-1}x]=24[ln x]+8[e^x]+6[cos^{-1}y]##. (##[.]## is the greatest integer function, e.g. ##[2.3]=2##, ##[5.6]=5##, ##[-2.5]=-3## etc)Homework EquationsThe Attempt at a Solution The...

Well I was reading this paper http://inspirehep.net/record/1409825 and came across this comment: My question is basically a statistical one... how can you make several fits using only 2 fitting functions? Or do they mean something like fitting with func1 in some ranges [a,b] with a,b varying...

g(t)=½( f(t)+f(-t) ) h(t)=½( f(t)-f(-t) ) show its 2π periodic so: g(t+2π) = ½( f(t+2π)+f(t-2π) ) why does -t become t-2π ? ½( f(t)+f(-t) ) = g(t) h(t+2π)=½( f(t+2π)-f(t-2π) ) ½( f(t)-f(-t) ) = h(t) is this correct? can...

Homework Statement Homework Equations no equations required The Attempt at a Solution [/B] a) The number of hours of daylight is a periodic relationship, because it repeats the same wave-like pattern over the course of 1-2 years. b) the period is the amount of time it takes for one cycle...

Homework Statement Homework Equations none The Attempt at a Solution Is this correct? Thanks.

Homework Statement 2. Homework Equations The Attempt at a Solution a) [/B]f(x) = -5x2 + 20x + 2 y = -5x2 + 20x + 2 Factor -5 from the first two terms: y = -5x2 + 20x + 2 = -5 (x2 – 4x) +2 Complete the square in the bracket: (1/2 b)2 = [1/2 (-4)]2 = (-2)2 = 4 Group the perfect...

Please guide why answers are different in following two cases and which one is correct? Case 1. sin-1 ( – 1/2 ) – sin-1 (– 1) = 7π/6 – 3π/2 = – π/3 Case 2. sin-1 ( – 1/2 ) – sin-1 (– 1) = – sin-1 ( 1/2 ) + sin-1 (1)...

Homework Statement Let σ : Z_11 → Z_11 be given by σ([a]) = [5a + 3]). Prove that σ is bijective. Homework EquationsThe Attempt at a Solution I am just wondering if I can treat σ as a normal function and prove that is bijective by using the definitions of one to one and onto.

Homework Statement check for linear dependecy[/B] f(x) = cosx and g(x) = xcosx 2 functions from R to R Homework EquationsThe Attempt at a Solution Why this is wrong: if i take the scalar a1 = 3, a2 = 1 i can do that since 3 is real, and a1 is in R. so 3f(3) + -1g(3) = 0 there for we have none...

Functions f,g from R to R. f(x) = xcosx, g(x) = cosx for x = 0, we get f(x) = 0, g(x) = 1. so for scalar t in R t(f(x)) + 0 * g(x) = 0 . ==> f(x) and g(x) are linearly idepenent. Is that right? if so in functions we search for an x that makes the function dependent?

Homework Statement What is the fundamental period of the expression sinx/sinx.can you guys please illustrate how to make its graph? Homework Equations Okay I know drawing graph can give me the period.Can the period be found by any other method? The Attempt at a Solution I'm told that the...

I was reading the wikipedia article on Lithium and noticed that it says: Trace amounts of lithium are present in all organisms. The element serves no apparent vital biological function, since animals and plants survive in good health without it, though non-vital functions have not been ruled...

I have two questions related Gamma functions 1. Finding ##\Gamma## analytically. Is that possible only for integers and halfintegers? Or is it possible mayble for some other numbers? For example is it possible to find analytically ##\Gamma(\frac{3}{4})##? 2. Integral...

Homework Statement Assume a particle with a wave function ##\psi(x)## such that ##-\infty < x < \infty##, that move under some potential ##V(x)##. Show that: a) two wave functions with same energies can only differ by a complex phase; b) if the potential is real, then you can choose the wave...

hello, in the task of finding the optimal phase covariant cloning machine, i have to maximize two functions of six variables :f1=a.C+b.D and f2=a.B+c.D , they are many constraints, but I've already used them to get to those expressions in the first place, the variables are real scalars and vary...

Hello, i am studying calculus and I am looking for a book or website that covers the following topics: -Real functions with vectorial variables (limits, domains, continuity, derivatives, directional derivatives, gradients) -Vectorial functions with vectorial variables (derivatives and...