Mathematics

Since everyone's posting questions here, I thought I'd post a nice question I got on my Analysis III assignment last week. It's a bit involved (and somewhat pointless) but I thought it was pretty nice for some reason: Let [math]f : [a,b] \to \mathbb{R}[/math] be a regulated function, and let [math](x_n)_{n=1}^{\infty}[/math] be a sequence in [math](a,b)[/math] such that [math](x_n) \to a[/math] as [math]n \to \infty[/math]. Show that [math]( f(x_n) )_{n=1}^{\infty}[/math] is a Cauchy sequence.

if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And, if you are up to it, heres another one...D is the differential operator (D-3)[x] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = …

I have asked this in other forums but I don't get much of a response. In what dimension does a shadow exist. I thought that as everything in our universe is made of atoms you could not construct a 2d object. However obviously a shadow is not comprised of atoms but of a deprivity of photons. You can measue the length and width of a shadow so is a shadow a truely 2 dimensional object. I don't think a shadow can have a volume. However thinking back how can a shadow exist in two dimensions because a shadow will lay across rounded objects and I think planar objects can not be twisted.

Im trying to solve this equation for along time I tries to use the formulas for power 3 but it ddint help I think it shuld be factoring the left side but I couldnt make it z^9-z'^9=9|z|^4 please help

Pigeon Hole Theory. Is it still relevant? How can we apply it to our daily lives and mathematics? What exactly is it about? Is it applicable only for numbers?

Two questions. They may be very simple and easy for you, but a brain flash. 1.the square root of 20 consecutive positive intergers have the same intergral number, find that number. 2.(a-b)(c-d)/[(b-c)(d-a)=3 Find (a-c)(b-d)/[(a-b)(c-d)]

Any number can be distinguished form another number by at least two basic properties, which are: a) Structure b) Quantity Let me show you a nice thing, for example, let us take number 26. Now we can show that this quantity has more than one internal structure, which is based on the base value that we are using: Number 26 represented by base 10: ^0- 0123456789 |||||||||| |_|||||||| |__||||||| |___|||||| Base 10 = |____||||| |_____|||| |______||| |_______|| |________| ^1- | | 1 0 …

how would I go about finding sin(10^40) ? [10^40 in radians]

I'm coming up to a stage where I need to write an essay about some topic in Mathematics. Now, before you ask, the purpose of this thread is not to say "omg he's trying to get us to write his essay n00b fs". I'm trying to look at particularly interesting topics in mathematics to formulate some kind of essay title - and no, I don't want you to give me titles. Contrary to some common misconceptions about students, I want (and need) to do this by myself. I've had a fair amount of mathematical experience now, but I'm struggling to find some topic I find interesting enough to write an essay on. If anyone has any suggestions, then that would be much appreciated.

Why can we integrate ln?

Ok. Let's say that there is a given function y=f(x) And if your inverse of f(x) is exactly the same as f(x). What can you say about the symmetry of the graph of f(x)?

Its the last round of a game show. You have to choose between three doors labeled One, Two, and Three. Behind each door is a prize. Now two of the doors contain goats while one of the doors contains a brand new car. Your asked to choose a door number. Lets say you choose 1. The Host then reveals a door other than the one that you choose, lets say that it is door number 3, and it has a goat behind it. You are then asked if you would like to change your choice to number 2 or stick with number 1. Now the riddle is, does this make a difference? Should you change your answer or stick with it? Have you all heard of this wierd puzzle? I have a book about it, but t…

What are all of the mathematical constants that we know of (and what are they used for). By that I mean numbers such as pi, e, y and golden ratio. And could somebody please tell me how to create mathematical symbols and formulas on this site? I know it's possible, I've seen people do it on this site before.

Hi , I need your help . I search on the web an algorithm that can solve an n equations system at n unknowns . Thanks a lot!

The problem is to convert 3m/s^2 to km/h^2. How do you do that again?

Nope, not another boring, theological quest to find the value of 0/0, but in fact to disprove its existence... The simple proof that 0/0 doesn't equal any positive, negative, or imaginary number, then for example: 0/0=1, then 0/0(2)=1(2), making 1=2, if 0/0=2, we substitute 1 for 0/0. Now 0/0=0, this doesn't hold, so 0/0 might as well equal 0, nobody knows. This can be proven to not be able to be disproven by: a = b a^2 = b^2 a^2 - b^2 = ab - b^2 (a+b)(a-b) = b(a-b) a+b=b b+b=b 2b=b 2=1; This would be true that 0/0 cannot equal 0, but on line 5, a+b=b, we can subtract each side to get that a=0, in which case nothing can be proven for 2=1 …

As we all know that multiplication of a number by zero results in zero. What happens if zero is multiplied by infinity

Is it possible to do the inverse Laplace Transform of a constant? I ask because I have a differential equation which I transformed, solved and now need to find the invers of. Unfortunatly my answer has a constant, and I don't know what to do about it!!! Thanks!

is the numbers between 0 and 1 infinite?

Does anybody have any good maths websites? Any kind would be fine, thanks

Its that time of year again, wasnt sure whether to put this in maths or in challanges, never mind. Have a go see what you think, mabye a new pair of jogging bottoms for the brain eh? Ill put my solution up in a week or so, with the answers. 1.A churchwarden lives lives on a farm which is 200 meters from the nearest point, Pm on a straight road. 800m from P along the road is a chruch. The church warden can walk at 6kmh-1 over his farm and at 10kmh-1 along the road. What distance from P must he aim to meet the road in order to reach the church as quickly as possible? 2.The verger has 9 pieces of chain; -0-, -0-0, -0-0-, -0-0-, -0-0-0, -0-0-0, -0-0-0. -0-0-0-, …

I read a book about Numerical Methods and I found that it is very interesting. Why does numerical method always be taught with engineering? I think it is quite useful in normal life.

gonna take a class next semester on toplogy and i was wondering what it was. The course description was...less than descripted, damn mathmeticians

Hey guys Im pretty much stuck on this problem and really need some help it may seem easy to most of you but I am finding it difficult Here is the question.... c) An annealed 50mm x 50mm square cross section 30%Zn/Cu brass bar is drawn by several cold working steps to a final Square cross section of 20mm x 20mm. The final cold worked bar must have Tensile strength grater than 360mpa Yield stength greater that 300mpa And Elongation (ductility) Greater than 15% Refer to Diagram below Describe the steps involved including the % cold work in each step & intermediate thicknesses required if a maximim of 70% cold work is allowed at each work step. …

Are there any advanced math programs on the web?