fourier jr

yeah I should have gotten pencil & paper. L'Hopital's rule is a good swiss-army knife of a theorem.

The 1st two are obvious by L'Hopital's rule (as someone said) & while I haven't really tried the 3rd one I think I'd just multiply the denominator by its conjugate. (multiply by sqrt(2x+1) + 3*sqrt(x-3) / sqrt(2x+1) + 3*sqrt(x-3) ) ie multiply by 1, but you've got to pick the right 1. hehe

But I thought that was Taylor's theorem? You want to find the Taylor series about x=0; that's all there is to it, right?

That's ok I think engineers & physicists would say infinite series of sines & cosines because that's how they learned it & that's how it's done in science. I did it that way too in a 'calculus-for-physics-students' course, but then I learned the more general way in a real math course this year. I don't think it's as well known.

WOW Fourier series in highschool! I'm in BC & I don't think anybody does Fourier series in highschools here. That's crazy. Well, if you want to learn about Fourier series look no further than Antoni Zygmund's epic 800-page "Trigonometric Series" (hehe just jokin') edit: a Fourier Series doesn't have to be an infinite series, nor does it have to be sines or cosines. My analysis text (by Pfaffenberger & Johnsonbaugh, Apostol's also uses this as a definition) says Let X = {x_1, x_2, .... } be a countable orthonormal set in an inner product space V and let x be in V. The infinite series sum( (x.x_n)*x_n, n=0..infinity ) is called the Fourier series (relative to X). The coefficient x.x_n (x inner-product with x_n) is called the Fourier coefficient of x. Maybe it would be better to just say that any periodics function can be represented as a sum of sines & cosines....

I think only a function can be continuous. Maybe what you mean is 'is a point connected' (which is just what it sounds like). In that case, a point like [0.9999999..., 1] is connected.

No from what I understand, cells know what's going on around them & can communicate with each other & are 'self aware' (something like that) to some limited extent, and it isn't just mechanisms or chemical reactions. The cells know what they're doing. The guy made it sound like the the people in the department here think it's just a silly crackpot theory, but there are small groups of people who work on it. I just thought it sounded kind of interesting.

but there is no largest prime number; there are infinitely many

I a guy I know (not me, I'm in math) believes in cel consciousness, which is basically says that cells sort of know what's going on around them & can communicate with each other (to a certain extent). He told a prof about it & the prof said the guy better not tell any other prof about it because it's not 'mainstream' or something. What does everyone think of cell consciousness?

Yeah what kinds of books are you interested in, like history, problems, etc

One of the most helpful calculus texts is Calculus: A Physical & Intuitive Approach by Morris Kline he's one of my favourite authors

i just signed up; i'm a 4th-yr student @ U of Victoria, BC, canada & I just want to talk math with people