even Definition and 650 Threads

It is a simple exercise to prove using mathematical induction that if a natural number n > 1 is not divisible by 2, then n can be written as m + m + 1 for some natural number m. (Depending on your definition of odd number, this can either be stated as "every number is even or odd", or as "every...

I apologize in advance if the answer to this is really simple; I often overlook simple solutions when something trips me up. For example, if f(x)=x2 and g(x)=x3/2, and g(f(x)) is therefore, after simplification, x3, why is that still an even function if x3 graphed under other circumstances is...

Hi I have been looking at some lecture notes inc the following example. Solve : y'' + ω^2y = (some even function) The particular integral is then found using Fourier series. As the function on the RHS is even this only includes cosine terms. The complementary function is found from...

I have a question that might have a complex answer. If time didn't exist could anything move or even happen?

Homework Statement Hey, I got an even number from my book trying to double check it so if you wouldn't mind I would appreciate some comfirmaion or denial. Find the volume of the solid obtained by rotated te region bounded by the given curves about the specificed line. y = x, y =0, x =2...

This is taken from Peter J. Eccles, Introduction to Mathematical Reasoning, page 17. This is not a homework because it is an example in the text. Prove that 101 is an odd number. The text has given a way of proving it and I just want to do it with my own approach. Prove that 101 is an odd...

Hi all, What is the Hamiltonian or main equation, that if you solve it, parallel universes are predicted? For example, the Dirac equation, if solved, predicts the existence of anti-particles. If You solve Maxwell's Equations, you predict there should be E & M waves. Solving certain...

Hello folks, I'm not even sure if this is the place to put this but with some luck it might be. I just have a general question about permutations. I understand the concept of even and odd permutations of a set of numbers, what I am hoping for is an easy way to figure out if (given a...

Homework Statement In order to show that if ##(\vec E (\vec x, t), \vec H (\vec x, t))## is a solution to Maxwell's equation then ##(\vec E (\vec x -\vec L, t), \vec H (\vec x-\vec L, t))## is also a solution, my professor used a proof and a step I do not understand. Let ##\vec x' =\vec...

Homework Statement Determine whether the following function is odd or even or none: $$f(x)=\log \left(x+\sqrt{1+x^2} \right)$$ Homework Equations The Attempt at a Solution For an even function, ##f(-x)=f(x)## and for an odd function ##f(-x)=-f(x)##. Replacing x with -x in the...

Hey, I know there's a sticky on top of the page kind of about this but I read through the thread and I have a pretty particular case that which isn't really addressed. I just finished my undergrad studies, received a B.A. a few months ago in May, and I was thinking about going to school...

Just want to verify ##e^{jx\cos(\theta)}## is EVEN function respect to ##\theta## as ##e^{jx\cos(-\theta)}=e^{jx\cos(\theta)}## BUT ##e^{jx\sin\theta\;}## is neither ODD nor EVEN because ##\;e^{jx\sin(-\theta)}=e^{-jx\sin(\theta)}\neq\;^+_- e^{jx\sin\theta}## Thanks

Hi all, Homework Statement I'm working on a problem related to an MRI signal equation. Essentially I want to derive an equation that can tell me the point at which f(x) is maximum. I have differentiated with respect to x and double checked that there are no errors. But now I am stumped at...

Hi, I wish to obtain the Fourier series of the signal in red (please see attached figure fig1_sine_plots.png). Basically, it is a full-wave rectified 3f sinusoid, where f = 50Hz. The blue signal represents a sinusoid with frequency f = 50Hz. In the following equations (please see attached...

I'm in high school, all honors/AP..etc, and I won't be able to take the physics course at my school for another year or two (I've tried to take it earlier, believe me). Anyway, I've always had a huge fascination with space and the world and how it works, with an larger interest in antimatter and...

Homework Statement 1) f(x+1)=f(x)+1 2) f(x^2) =(f(x))^2 let a function real to real satisfy the above statements then prove whether the fuction is odd or even. Homework Equations The Attempt at a Solution using the 2) we get 1) f(0) = 0,1 2) f(1) = 0,1...

Homework Statement Calculate the wavelength of the Lyman-α line (the transition from the 1st excited state to the ground state) for (a) hydrogen atoms and (b) positronium e+e-, and explain the origin of their difference. In the light emitted from a star, a pattern of emission lines is found...

Hi guys! I had a recent talk with my friend about my college debt / tuition and future job prospects as a means of paying off that debt and he voiced his concerns about my future financial state, concerns which hit me square in the face and brought me back down to reality - now I just can't stop...

Is f(x)=\sin[a(b+|x|)]\;\hbox{ and }\; g(x)=\sin[a(b-|x|)] Both EVEN function? It looks even function to me even though it's a sine function( odd function), but the |x| make it an even function where f(-x)=f(x).

Homework Statement Prove the following theorum: If V(x) is an even function (that is, ##V(-x) = V(x)##) then ## \psi (x) ## can always be taken to be either even or odd. Hint: If ## \psi ## satisfies equation [1.0] for a given E, so too does ## \psi (-x) ## and hence also the odd and...

Hello, this is my first post :). I am a high school sophmore and am incredibly interested in physics... My school gives an intro-physics course for those who want to pursue it. I got over a one hundered average in that class, I have a 3.83 (out of 4) gpa. I also got advanced on the "MCAS"...

When creating a Fourier series for a function f(x), I consider whether the function is odd or even first. Yet, often these functions are in the positive region [0, L] . Since f(x) is only defined in this region, can I change the function to get a desired parity? By example, my concern...

Homework Statement Let f be integrable on the closed interval [-a,a] If f is an even function, then \int^a_{-a}f(x)\,dx = 2\int^a_0f(x)\,dx Prove this. Homework Equations The Attempt at a Solution The solution is given in the book. Because f is even, you know that f(x) =...

Is the integral of an even function an odd function and vice versa? I know the derivative is.

I would like to create a series where for each term if n is odd the term =1 and if n is even, the term = 2. I.e. a_{n} = 1 if \ n \ is \ odd \ and \ a_{n} = 2 \ if \ n \ is \ even

Homework Statement Is there a general formula for the sum of such a series (or can it be self derived) ? 2^2 + 4^2 + 6^2 + 8^2 ... N^2 (all the way till some even number N) Homework Equations \sum r^2 (from r=1 to r=N) = 1/6 * n(n+1)(2n+1) The Attempt at a...

I wanted to start this thread as kind of an offshoot of the "best songs ever" thread. The spirit of this thread is to post cover versions of popular (or even not so popular) songs that you think are better than the original (or that you just really like:-p) As a part-time songwriter, doing a...

How are even and odd functions defined in n-dimensions? In my homework, we had to integrate f(x,y,z)= (x^2)z + (y^2)z + z^3 over a sphere centered at the origin. My answer came out to be 0 and I made the guess that it might be because f(x,y,z) was an odd function. Now, I don't know if this is...

Homework Statement A customer is choosing between two cellular phone plans. One plan has a monthly fee of $50 for an allowance of 500 minutes per month. If the customer uses more than 500 minutes, the charge is $0.35 per additional minute used. The other plan has a monthly fee of...

I am coming across hiccups in my proof process. I am given this problem - Prove: if n is an integer and 3n + 2 is even that n is also even. I have to apply a contrapositive proof to this problem. The form is then \negq therefore \negp .The problem becomes - if n is odd, prove that 3n+2 is even...

SA + SB always give pH= 7 even if concentration of SA is a lot bigger than SB? let's say 10 M of HCl react with 0.1 M of NaOH, is the pH at equivalence point also 7?

An electric field is E = 250 N/C i for x > 0 and E = -250 N/C i for x < 0. A cylinder of length 20 cm and radius 3 cm has its center at the origin and its axis along the x-axis such that one end is at x = +10 cm and the other is at x = -10 cm. What is the outward flux through each end? a) +x...

The DCT of an even function is comprised of just cosine coefficients, correct? I'm playing around in MATLAB and I came up with a simple even function 1.0000 0.7500 0.5000 0.2500 0 0.2500 0.5000 0.7500 1.0000 0.7500 0.5000 0.2500 0 0 0 0...

I am not a teacher or even student of physics but I am translating a physics paper into English and I need some help. I have a sentence that may translate as follows: "Newton introduced m-dependency upon taking into consideration, within the context of his second law, the experimental fact...

I just finished my last physics class (e&m) and I was pretty intrigued by capacitors and their ability to store charge. I decided to take an electronics class next quarter so I bought a few things including breadboard, capacitor, resistor, diodes, motors, and so on. Now...I have a 50V 1000uF...

There was a question but I figured it out. $$ g(\theta) = \begin{cases} \theta, & 0\leq\theta\leq\pi\\ \theta+\pi, & -\pi\leq\theta < 0 \end{cases} $$ So $g_e=\frac{g(\theta)+g(-\theta)}{2}$ and $g_o=\frac{g(\theta)-g(-\theta)}{2}$ \begin{alignat}{3} g_e & = & \frac{\begin{cases} \theta, &...

Let me explain. Suppose I wanted to make the argument that we need more nuclear weapons. Sounds absolutely crazy, but based on some theories (I don't agree with) the more strength you have to more peace you will have. Can someone give me an example of anything else related to...

I recently saw an Elon Musk talk on YouTube where he commented on how if Earth's gravity were just a little stronger, then it would have been impossible to generate enough thrust to get into space. He cited that as the reason why only a handful of national governments have successfully reached...

In my book I need to prove the general theorem that I can always pick the eigenstates in the time independent Schrödinger equation to be either even or odd ψ(x). This provides that the potential is an even function and is not hard to show if you use that if ψ(x) is a solution then too is ψ(-x)...

Homework Statement Let (G,*) be a finite group of even order. Prove that there exists some g in G such that g≠e and g*g=e. [where e is the identity for (G,*)] Homework Equations Group properties The Attempt at a Solution Let S = G - {e}. Then S is of odd order, and let T={g,g^-1...

1. Prove product of 3 consecutive naturals is even data i just want to know if this proof is acceptable, or is there a simpler proof. The Attempt at a Solution Proof: suppose if the product 3 consecutive naturals is dividable by 2 then it is even. Base case: n = 1 n (n + 1)...

why poles of machine are always even?

Homework Statement Prove that the product of two consecutive natural numbers is even. 2. The attempt at a solution Hi, I'm just starting to work with proofs by induction, I'm just wondering if this is a valid technique, and/or if I am being too verbose in my proof, thanks! Let...

1. (sin4x + cos4x) Homework Equations The Attempt at a Solution (sin4x + cos4x) = (sin4(-x) + cos4(-x)) = -sin4x + cos4x im thinking it is an even function

even in darkness there is light ! this could be a stupid question but i hope i can get an answer of some sort . can the quote even in darkess there is light be proven? can there be light paticules waves photon or anything else in darkness thank you in advance

Homework Statement If a is even, prove a-1 is even. Homework Equations We know that every permutation in S_n, n>1 can be written as a product of 2-cycles. Also note that the identity can be expressed as (12)(12) for this to be possible. The Attempt at a Solution Suppose a is a permutation...

Hello I have a theoretical question. When I check if a function is odd or even, I usually check: f(x)=f(-x) or f(-x)=-f(x) someone told me today that before checking it, I first need to check the symmetry over the Y axis, and if the function is not symmetric over Y, there is no point of...

Homework Statement I know you could prove this by stating every integer is either 3m, 3m+1 or 3m+2. However I am trying to prove this just using either even numbers or odd numbers. so for example, when I try: (2x+1)^2 = 4x^2 + 4x + 1 - expand = 3x^2 + x^2 + 3x + x + 1 - group like...

Homework Statement Let f: R → P(R) given by: f(x) = {y ∈ R; sin y < x}. If A is such that f(x) = R for every x ∈ A, then: (i) A = [-1, 1]; (ii) A = (-∞, a] for every a < -1; (iii) A = [a, ∞) for every a > 1; (iv) A = (-∞, a] for every a ≤ -1; (v) A = [a, ∞) for every a ≥ 1...

Homework Statement Show that function is even or odd: (x^2|x-1|)/(SQRT(x-1)^2) Homework Equations The Attempt at a Solution (-x^2|-x-1|)/(SQRT(-x-1)^2) After this i don't know how to procede.