Math Is Fun Forum

Oh come on who uses both of their hands, this is where it's at

http://www.youtube.com/watch?v=vnRJROskpp4

Is this a homework assignment for a class? If so, what class? Are there any limits of integration for this integral? This integral is known as a Fresnel integral. If the integration is done from 0 to ∞, it's not very hard to calculate the integral if you know what the gamma function is. There isn't really much to do with this if it is an indefinite integral though.

I use a program called WinShell to type my math papers. It's a free program that you type text and LaTeX into and it will make it into a PDF or PS file. If you want to try it out you'll need Miktex too:

http://www.miktex.org/
http://www.winshell.org/

You'll need to know a little more about LaTeX to make a document, but there is a demo file included with WinShell that you can use to get started.

As for understanding topology, it may be best for you to take an actual course on it instead of self-study. Have you only been learning it from Rudin's text? Perhaps you should look into chapter 3 of Apostol's "Mathematical Analysis" or the Munkres text "Topology". If you want a free topology resource, consider this online text:

http://uob-community.ballarat.edu.au/~s … opbook.pdf

It's probably the most basic introduction to topology you'll find. If even that is hard to follow, you might just need a teacher. It is sometimes easier to see what's going on when someone else is writing it on a board in front of you.

No, Chocó really is a cannibal.

Silly me, if a function f is differentiable at c, then f is continuous at c. Hohoho, good teamwork *high fives*

I suppose it is the same logic, but of course they have to write the proof SOMEWHERE in the book, since the chain rule is such a common thing, and it's not just a direct corollary. Which reminds me that I hate when a book states a less popular theorem and says "see this author for a proof".

One reason they are shorter is because they use another theorem or two previously stated in the same chapter. They're definitely not imprecise or informal. Could you give me an example of a lengthy chain rule proof?

Thanks for pointing that out Jane, you have been reported

Ok, how about this then. If you post DIRECTLY after the post you are commenting on, you don't need to quote them. If it is the first post in the thread, it is obvious who you are talking to, and if it isn't, you can say "^", "To the above poster" or "@someone" to get their attention. If you absolutely need to quote something someone said, then just quote that part (like what I just did in this post). Surely all the smilies and such in the post aren't important things you need to quote. I'm sure this shouldn't be a problem for you since it isn't your intention and you're so against small posts intended to raise post count.

Is it going to be possible sometime in the future to make quotes not count towards your post count?

Also, rida, I think the intention was irony. And if justlooking's intention wasn't so, mine was. I thought it was funny for a one time thing

1. To make this simple, let us see if we can do the problem with only two reciprocals, so 1/2006 = 1/a + 1/b, with -2006 < a, b < 2006. Multiplying both sides by 2006ab gives ab = 2006a + 2006b. We manipulate the expression so that we can factor:

Since -2006 < a, b < 2006, we have that 0 < 2006 - a < 2 × 2006 and 0 < 2006 - b < 2 × 2006. So we want two factors (2006 - a and 2006 - b) of 2006² that are between 0 and 2 × 2006. We know that 2006 = 2 × 17 × 59. So our factors are 2² × 17² (= 1156) and 59² (= 3481). Then 2006 - a = 1156 and 2006 - b = 3481, so a = 850 and b = -1475. Thus

2. You're perfect so far . The next step is to realize that 5 times the digits of our number (I'll call it N) must be divisible by 25, since 5 is its last digit. The multiples of 25 end in 00, 25, 50, or 75. Since N can't have 0 or an even number as a digit, it must end in 75. Once again, since N is 5 times the product of its digits, it is divisible by 5 × 7 × 5 = 175. Starting at 1 × 175, every 4th multiple of 175 ends in 75. So 1 × 175 = 175, 5 × 175 = 875, 9 × 175 = 1575, ..., 57 × 175 = 9975 (we stop at 57 since N must be less than 10000). If you write out all these products you see that the only numbers there with only odd digits are 175, 1575, 5775, 7175 and 9975. By direct calculation the only one of these which is equal to 5 times the product of its digits is 175.

You will get a calculator for this test, right? It might be a little tedious to do this all by hand.

I used the logarithm property