even Definition and 650 Threads

Homework Statement Suupose that f(x) is an even function of x. Does knowing that lim as x approaches 2 from the left of f(x) = 7 tell anything about either limit of f(x) as x approaches -2 from the left or the limit of f(x) as x approaches -2 from the right? Homework Equations...

Homework Statement For all natural numbers, a and b, if a and b are both even, then (a^2+b^2) is not a perfect square. (prove this) Homework Equations The Attempt at a Solution I tried proving by contradiction and got (2s)^2 +(2t)^2 =k^2. which translates to 4s^2 +4t^2=k^2. I...

We have E the set of even integers with ordinary addition Define new multiplication * on E defined as a*b = ab/2 where on the right hand side of the equation is just normal multiplication. I am just a bit confused i am trying to show Associative multiplication meaning i have to show (a*b)*c =...

Homework Statement Let's say that my friend throws a tennis ball down a building. is it possible for me to find the time at which it hits the floor and at what speed it it is when it hits the floor. If he only tells me the initial speed and length of the building? 2. The attempt...

Hello, When the Celsius temperature was first defined, it was defined by saying that 0°C was the freezing point and 100°C the boiling point. Now, this is far (infinitely far, actually) from a definition of temperature (this was before the 2nd law or Stat. Mech.; they are not important for our...

Hello .. I'm currently trying to choose my degree course and I'm having difficulty in knowing what to do. I know this will sound stupid but I'm terrified of taking IT and/or Science in University and failing in it. Technology in particular because Maths is hard to me and many if not all IT...

Homework Statement Let f: R\rightarrow R be a differentiable even function. Prove that f' is an odd function. Also, prove that if f is a differentiable odd function, then f' is an even function. Homework Equations The Attempt at a Solution I tried to use definition, so I should...

Homework Statement The force exerted by the wind on the sails of a sailboat is 490 N north. The water exerts a force of 250 N east. If the boat (including its crew) has a mass of 250 kg, what are the magnitude and direction of its acceleration? Homework Equations V= SQRT(X2+Y2)...

Part 1 (Skip this if you would rather get to the point) Long story made short I'm an individual that was failed in the worst possible way by the US education system. I found school to be really basic, learned to read, early was really good at math, then school turned into repetitive nonsense...

Homework Statement I know for graphs of function f(x)=x^n where n is an odd power, even power or square root have their own pattern but how about f(x)=x^(3/2) or f(x)=x^(1/2) is that considered odd or even ? Homework Equations The Attempt at a Solution

I don't know if anyone has heard of these even more elementary particles, http://en.wikipedia.org/wiki/Preon There even more fundamental than quarks, i was wondering if they are well excepted into the scientific community or if its a very unlikely that they are real.

I know this sounds silly but hear me out. I'm a second year uni student intending to major in physics and I was going fine with physics until the start of the year when I encountered Atomic, Nuclear and Condensed Matter Physics(ANCMP). I tackled it again and again dedicating long periods of time...

I'm wondering right now if my undergraduate education really is for the purpose of learning about the world and myself, or if it's some pre-X feeder in which I'm supposed to work in order to attain certain credentials, and use those credentials to enter another feeder program whether it be...

Homework Statement Let f_1(x) and f_2(x) be odd and even functions respectively. How can we construct an even function out of these? Homework Equations f_1(x)=-f_1(-x) f_2(x)=f_2(-x) The Attempt at a Solution

Is this function odd or even: f(x) = 6x(1-x)

I am a senior in high school and I am taking a college class at a local community college. After this year, if I decide not to take the transfer credit, can I reject it? So I can take the course again at my new undergrad again? Like basically abandon the transfer credit and grade? Will my...

I mean, several light years from here, is it possible to distinguish between the signals coming from Earth and the massive amount of electromagnetic radiation emitted by our Sun? From a great distance, every solar system must appear dot-like. Is it possible that civilizations are actually...

So I have been teaching myself some c++, and as I tried to do an example my guide book showed me: that is where things went awry. The book I have been using is Programming:Principles and Practice Using C++ By Bjarne Stroustrup. I used the solution for the example where I got stuck on a certain...

If I have \int_0^{+\infty}h(x)g(x)dx=0 where h(x)>0 in [0,+\infty]. Can I conclude that g(x) might be zero or an odd function in such interval? If the condition above is still valid and I add this request: g(x)=(f(x)-q) where f(x) is positive function in the interval. Can I say that g(x)...

Homework Statement should be my last question for at least the next few days...here goes... Prove that, for even powers of sine, \int^{\frac{\pi}{2}}_{0}sin^{2n}x dx = \frac{2\cdot4\cdot6\cdot...\cdot(2n - 1)}{2\cdot4\cdot6\cdot...\cdot2n}\cdot\frac{\pi}{2}Homework Equations uv - \int v du...

Hey, So I am currently trying to workout the fatigue characteristics of my Formula Student Space frame design, I am using Cold Drawn Seamless mild steel. I have the following mechanical properties: Re - 360 MPa Rm - 450 MPa I think these are the effective stress intensity range and...

Homework Statement Prove that every palindromic integer N in base 10 with an even number of digits is divisible by 11. Then prove that every palindromic integer in base k with an even number of digits is divisible by k+1. Homework Equations palindromic means the number reads the...

I just finished a course where we discussed concepts such as Lebesgue integration and Lebesgue measure of sets. Today, I was telling my brother about how the irrationals on the interval [0,1] have measure 1, which is sort of counter-intuitive. Anyway, he proposed the following question. Let A...

Homework Statement Integrals of this type: \int \frac{1}{\sqrt{2E-2(\frac{1}{r}-\frac{1}{2})+e^{-r^2-z^2}}} dz does anyone know where I can find it? Homework Equations The Attempt at a Solution

Can anyone tell me what's the formula for even and odd number multiplication. For example, what would be the product for 2 x 4 x 6 x 8 x 10 ... x 100 and what would be the product for 1 x 3 x 5 x 7 x 9 x 12 ... x 99? I am trying to solve a problem which asks me to prove that 1/2 x 3/4 x 5/6 ...

Homework Statement Show f(x) can be expressed as the sum of E(x) and an odd function O(x). f(x) is defined for all x (assume domain D symmetric about 0) f(x) = \frac{f(x)+f(-x}{2} Then: How does it look if f(x) = e^x? Homework Equations N/A The Attempt at a Solution So I...

Hi I know that stationary states in a system with an even potential energy function have to be either even or odd. Why does the ground state have to be even, and not odd? This is asserted in Griffiths, page 298.

Homework Statement Evaluate the limit analytically if necessary using L’Hopital’s rule: lim x->0 (1+x)1/x Homework Equations The Attempt at a Solution Well, I can get the thing equal to 1 if I just plug in zero, so do I need to use L'hopital's? This whole thing is very confusing...

Homework Statement Prove if f(x) is defined on -L< x < L, and if f(x) is odd function on (-L,L), the f'(x) is even function. and vise versa. Homework Equations Using Fourier series expansion, f(x) is odd function on (-L,L) can be represented by Fourier sine series expansion. If f(x) is...

HOw do you integrate sin(x)^10?

I am having the hardest time proving that "The product of any two even integers is a multiple of 4." My proof seems to be going in circles! Any guidance would be amazing!

Hello people. I'm a freshman in college and I'm looking forward to enter an advanced mathematics program. The admission test is basically number theory & sometimes I get stuck with some questions (I'm using Spivak's Calculus to study). I'm stuck on question 8, chapter 2. "Prove that every...

So I am aiming to prove that phi(m) is always even if m>2. What I have thus far If n is an integer such that (n,m)=1 where 1<n<m then (m-n,m)=1. Note: If (m-n,m) are not coprime this would imply that m-n divides m. This is a contradiction. Now, consider the case where m is even and n=m/2...

This is the one occupation that I'm sure I would love, but the more I read on it, the more impossible it seems that I will land a tenured university position. I'm a 1st year student at Michigan State and have a 3.9 at the moment. I imagine I'll end up in the 3.75+ area after my physics...

Hi guys, Not actually a mathematics question as such (sorry) but does anyone know where i can get my hands on a copy of Chen's paper "On the representation of a large even integer as the sum of a prime and the product of at most two primes". For the life of me all i can find is references to it...

Homework Statement If f:(-a,a)-->Real numbers, then f can be rewritten as the sums of an even and an odd function Let k: Real numbers\{-1}-->Real numbers be given by k(x)=\frac{x^2+4}{x+1} (i) Prove that there is no interval (-a,a) on which k is either even or odd (ii) Find an even...

I've seen this exact question in a book. (This is not homework) I've always thought this is because work has nothing to do with effort, but seeing this question on a book quite shocked me actually, is there any deeper explanation?

Find the mass of one turn of wire in the form of a helix with a linear density e^(-z) in lbs/ft. Would I write as <e^(-z)*cost,e^(-z)*sint, t>? Maybe?

Homework Statement f(x) = sin(x) for 0\leqx<\pi. Extend f(x) as an even function . Obtain a cosine Fourier series for f. Homework Equations a_{0}/2 + \sum a_{n}cos(nx) The Attempt at a Solution So as far as I know, to extend sin(x) as an even function you have to make f(x)=-sin(x)...

From what I have read out there, of the four fundamental forces that have been detected in our universe, gravity seems to be the weakest at the atomic level and smaller. I figure this is most likely true because at the atomic level and smaller - the weak and strong forces (those causing beta...

I'm going to fail my first proofs class. How do people even learn this!? A bit of cheese with my whine perhaps but I'm more frustrated because I don't know what to do. I am going to fail this class unless I figure it out before our first exam. I read the chapters, take notes, try to understand...

Homework Statement There is a charged wire aligned/centered along the Y 2L in length. A test charge is placed D distance from the wire on the X axis. The wire has a total charge of Q. calculate the integral to figure out how much force the test charge experiences. a semi decent pic of the...

I've been trying to understand some basic stuff about cosmology for years, and I still can't quite get there. I'm not even sure which part of it I'm misunderstanding, and don't know what questions to ask, so I'll just start blasting out the questions and see if anyone can help me make sense out...

Homework Statement Suppose x = (x1, x2, ..., xn)T ∈ Rn is a random vector drawn from the n-dimensional standard Gaussian distribution N(0, I), where 0 = (0, 0, ..., 0)^T (0 vector transpose) and I is the identity matrix. (a) What distribution does ||x||^2 follow? Justify your answer. (b) On...

I know it's a dumb question but I can't figure out why the totient of n is always even (I've read in a book that it "follows immediately from the definition of the totient function", so it should not require any theorem to prove). It is clear to me that it holds true for n = pk, where p is a...

if god is omnipotent, could even he make a rock so big that he could not move himself?

I was at a new year's party and the people who hosted it own a cat. Apparently, I'd been sitting on its chair and I got mewed off. How rude! Stupid creature. Question to you guys: How do you even like cats? They are such arrogant creatures. The look they give you seems to say "Listen human! I...

\varsigma(s) = \sum^{\infty}_{n=1}n^{-s} If you substitute a trivial zero, let's say -2. Wouldn't it be \varsigma(s) = \sum^{\infty}_{n=1} = 1^2 + 2^2 + 3^2 + 4^2 + . . . How would this series be equals to zero? Thanks

Determine all possible even perfect number(s) C such that each of C-1 and C+1 is a prime number.

Homework Statement Given that n independent tosses having probability of p of coming up heads are made, show that an even number of heads results is 0.5(1+(q-p)^n) where q is 1-p, by proving the identity Sigma from i=0 to n/2 of (n choose 2i) (p^2i)(q^(n-2i))=0.5(((p+q)^n)+(q-p)^n)...