Dave

I don't know. My definition of the derivative appears to be the same in both threads (although the latex is garbled in one of them). I'm also going to knock the size of these latex images down, because they're huge

Pretty much. You might see it written like this: [math]\forall \epsilon > 0 \exists \delta > 0 \text{ such that } | x-a | < \delta \Rightarrow |f(x) - L | < \epsilon[/math] (using universal quantifiers). Translated into English, this reads: "For any epsilon > 0, there exists a delta greater than zero such that..." and the rest is the same.

Any bugs: please let me know and I'll try and fix them asap. You can now write matrices properly without & appearing all over the place [math]\left(\begin{array}{cc} a & b\\ c & d \end{array}\right)[/math]

Aerodynamics is a bit tricky to analyse mathematically because you're going to have to use a lot of fluid dynamics. Your best bet is to compare things experimentally.

Okay, but the rest of the thread is rather perplexing

How about pathways in processor chips? High-temperature superconducting materials in new CPUs would dramatically increase performance with no heat loss - no heatsink required

It's fairly simple; 4n/3n-1 = 4*4-1 * 4n/3n-1 So we have: 4*4n-1/3n-1 = 4(4/3)n-1.

For the record, 2^(10^11) is a much larger number than the one you've stated.

It would help if you gave us the integral you're trying to evaluate

The way to approximate them is to use Taylor expansions, but I daresay you probably haven't done those yet. So, in a word, probably not

Looks to be right to me.

Try rephrasing your post to include some manners and politeness. As for the actual problem; the first should be fairly obvious. The second is trickier; you can see that x = -2 yields an undefined value for g(x). This should give you a clue as to how to find the domain

I found that it didn't really make sense when I did it, but looking back on it after a year (and after you've had chance to pick up on all of the little hints), it gets a lot easier. I had the same kind of problems - I think more or less everyone does.

You need to show the derivation really; we can't help without it.

Not really. The only people who tend to disagree are those who don't like the definition (or maybe even concept) of the limit. Personally, I think it's a great definition.

Well, unless a capacitor decides to explode whilst you've got your head near it. But you shouldn't be putting your head inside a computer that's on

No.

I don't really care to think about this from a physical viewpoint, as I've already mentioned.

No, I'm saying you can't do that. Which is kindof my point.

It's not going to be secure unless you can encrypt it properly. The only encryption technique that I know of which isn't one-way and is "secure" is RSA, and for that to be secure, you need a public key to be stored somewhere else where it can't be found.

Then why do you ask? Look at it this way: it's useful for you to think of dy/dx as a fraction. However, it's clearly not. d/dx is an operator, and you can't just play around with dx like it's a triviality. This is just getting silly. This is the last time I will say this: I do not care about time, or any other physical quantity. If you refuse to acknoweldge this, then I'll just stop replying. It doesn't really look like you're listening to me anyway.

No, that's the definition of a limit.

I absolutely love this:

This is obviously rubbish, hence I'm moving it to pseudoscience.