Mathematics

Hey, i am stuck on this question, although i think i have done a bit of it already... here is what i have done so far.... we want an [math] N_\epsilon [/math] such that if [math] n \geq N [/math] then [math] |\frac{1}{x_n}-\frac{1}{x}| \leq \epsilon [/math] we know (by the denition of a limit of a sequence) [math] |x_n - x| < \epsilon_2 [/math] now [math] |\frac{1}{x_n}-\frac{1}{x}| = |\frac{x-x_n}{x \times x_n}| = |\frac{x_n-x}{x \times x_n}| = |x_n-x| \times |\frac{1}{x \times x_n}| [/math] so [math] |x_n-x| \times |\frac{1}{x \times x_n}| < \epsilon_2 \times \frac{1}{x \times x_n} [/math] but i am unsure of what to do next. …

Using a stopwatch, a stick, a ruler, and a shadow cast by my house and the sun, I estimated the apparent speed of the sun. Or so I thought. I ended up with a rough number of 75 mm in 5 minutes. Now, doing the math, we get 900 mm in and hour, and 21,600 in a day. That means the sun's light apparently travels 2,160 cm in a day, or 21.6 meters. This can't be right. Can anyone tell me what I did wrong?

Hey guys, well, my math problem is below and I need help on it: Determine the maximal subset of R(real numbers) on which the following functions are (i) defined (ii) continuous [math] [x] [/math] is a Gauss bracket of [math] x [/math]. Defined to be the greatest integer (Z) not greater than [math] x [/math]. Eg: x=1.7, [x]=1

OK, after reading books on linear algebra, and vector calculus, I have come to tensor transformations. Huzzah! However, I do not have any book to study from(!) so I am rather "sol". I do understand that covariant tensors have subscript lettering and contravariant tensors have superscipt lettering. How do I transform a given vector in covariant and contravariant tensor transformations? I googled it and there were a number terrible websites. Any help would be great!

hey, its been awhile since i could do these, could i have a little bit of help, if there is someone willing out there? Cheers Sarah

hi finding these questions impossible and was wondering if anyone knew how to answer them!!!.... 1) a linear transformation T:R^6 -> R^6 is known to have characteristic polynomial x^2(x+1)(x+5)^3 determine all possibilities for the minimum polynomial of T 2)let V be and inner product space over C with inner product <,> and let u,v be vectors from V which are orthogonal to each other. prove that ||au+bv||^2 = |a|^2||u||^2 + |b|^2||v||^2 for any complex numbers a and b thank you!!!

What exactly is infinity? Isn't it just a term to describe a number that is beyond our calculation ability? Since the numbers go on forever, wouldn't it be impossible to have a value that is too big to be a number?

Recently I've been reading up on QM and came upon the lovely little thing known as the fourier transformation. I was able to tell that it involved calc, and my physics teacher explained what it did, but does anyone know exactly what level of mathmatics is involved in it? or the specific subjects needed to understand it?

umm here is the question "Here V is a nonzero finite-dimensional vector space: If dim V = p and if S is a linearly dependent subset of V, then S contains more than p vectors. True or False?" Now i am not sure , i could argue either way, although the answers says that it is false. i think it is false because it doesnt say that S is a basis, and so S can have less than p vectors and still be a subset of V. on another note, can a z-dimensional vector space V have a basis with less than z vectors in it? (or is this a related note? )

would anyone be able to give me a hint to get me going with this problem, i am unsure as what i should start by doing... small hint? Cheers Sarah

Hello... I am currently doing my U.G in electronics... However I am suffering with a networking course which has a tinge of graph theory in it. I feel my graph theory skills should be optimised, but i fail to find a good book which deals with the subject and its networking applications with sufficient rigour. Could anyone direct me to one?

I figured since I don't want to clutter up this board with a bunch of newly created threads, that I'd post whatever math problems I'm having in here. I suck at math, sadly. The most recent problem I've come across is this: factor each expression completely x^3 - 8y^3 So I tried doing this since: (x-y)(x^2 + xy + y^2) factored: x^3 + 2x^2y + 4xy^2 - 2x^2y - 4xy^2 - 8y^3 Which turns out to be: (x -2y)(x + 2xy + 4y) what I don't understand from this problem is how 4 gets there.

I am sure this is very simple, but could someone work through this question for me? This is not homework, I just want to learn the steps to do it. x = (4-i)/(1-3i) I am supposed to put it into the form x = a + bi The answer is: x = 7/10 - 11/10 i Thanks for any help you can give me.

hey i was just wondering how you show this... or well if i am doing or done it right? thanks -Sarah ...i'll post my answer in a min, just let me type it up...

i can't quite work this one out... i think the first step is to say that we want to find complex root of this: z^{n} = a but yeah...i dunno...can someone give me a few pointers please Sarah

Right, Aparantly the chance of England not winning the test today is approx 2-1 Now, in theory that means in say 3 matches England would not win 2 and win 1. But what are the chances of the afformentioned situation occuring. In theory they are certain, but evidently that is not the case.

yay! i might have actually got this one right hopefully, how'd i go... i reckon R = 2 , where R is the radius of convergence of the power series....

hi, yet another one of my questions i can't quite figure out how to prove this....i can see its true, but i just don't know how to write it out formally :S -Sez

Ok, i got a couple of probs. how do i prove if a series is divergent or convergent? and what is the nth term test? can someone please explain it to me?

I don't know the latex symbol to get long division symbols but hopefully someone can figure this out for me. I've been doing pretty good until I came across this problem: (x^3 + 1 + 2x) / (x^5 + 3x + 2) Answer is: [hide]x^2 - 2 + [(-x^2 + 7x + 4) / (x^3 + 2x + 1)][/hide] I was going to go in depth about this, however, I don't see the latex symbol that closely looks like the square root symbol for division.... It's very obvious to me that I need long division. I just didn't know how to solve the problem, that's all. I don't understand the long division processes used in this. Long division in plain numbers is somewhat easy, however, this p…

Here's a maths question I have found in a maths test. Solve for x. Give me some hints please...I am clueless. Anyway ignore those green squares.

hi all , i can't figure out how i am ment to use the stated fact about tan x. the way i'd do it is dividing the series expansion for cos(x) into that for sin(x)... but yeah i dunno any advice would be greatly appreciated __sarah__

i am new to this forum and not exactly sure if this post belongs here. i need a concrete idea for a determinant. i understand the determinant as the volume of the parallelopiped in the n dimensions corresponding to the order of the determinant. but is there an alternate idea? while working with polygonal numbers and determinants i found that the 3*3 order determinant of any 9 consecutive n-polygonal numbers is -(3*(n-2))^3. i was trying to understand what this result could mean but since my idea of the determinant is vague i was trying to go backwards and understand the determinant. anyway does this result have anysignificance? i proved this by obtaining a general form…

This is the problems on the 46th International Mathematical Olympiad. My friends got excellent result from it, some of them are still very young, the youngest is 2 years smaller than me. That could depress me much. [as I even could not get the qualification to join the competition] http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/1dayenglish.pdf http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/2dayenglish.pdf

hey guys could i get a hint at how to do this problem please? i just can't quite work out what my first step should be,.... Thanks -Sarah