Dave

We can basically add any package that's included in TeXLive 2009.

Thanks I spent quite a lot of time tweaking the image settings this time around so the output now looks quite nice.

Whilst you can use implicit differentiation, I think the OP is more interested in how you obtain this from the limit definition of the derivative. Having said this, I'm not 100% sure how to do it directly from the limit. The way you might approach it is to evaluate [math]\lim_{x\to 0} \frac{e^x-1}{x} = e^x[/math]. This follows immediately from the Taylor series definition of [imath]e^x[/imath]. Then re-write [math]a^x = e^{x \ln a}[/math] and apply the chain rule.

Can you post a screenshot of the issues you're having? Or is it a speed issue?

Turns out that it was just a simple error. Now fixed, at least for new posts - you will need to edit your post to see changes. Edit: Even unedited posts should now be working.

Good question. This is on the urgent to-fix list.

Yup, I agree completely about the post icons. It's on the list already, I really don't like the default ones either. However, we thought it was more important to get everything over to IPB and then continue a process of refinement from the input of you guys than waste lots more time on an and old (and unpatched) version of vBulletin.

You'll need, for example: [math]\sqrt{x}[/math]

Over the next couple of days we will be posting a list of new features you can find on the forums; until then, enjoy playing around!

Just a quick note to say that we encountered a few problems in the test conversion that we need the guys behind IPB to fix, so we're waiting on that at the moment. However we may eventually lost patience and fix them ourselves (if I can figure out how it works ).

11th order Runge-Kutta is going a bit far. Most people only use up to around 4th order. Beyond that, you should be using a spectral type method if you want higher order accuracy.

Simply that you've not done the multiplication right. [math] 3 \, \mathrm{m} \cdot 5 \,\mathrm{m} = (3\cdot 5) \mathrm{m}\cdot \mathrm{m} = (3\cdot 5) \mathrm{m}^2 [/math] and the rest follows.

Good problem! I'd originally thought you weren't along the right lines, but now I've studied things a little better (and jogged my memory regarding supremums ) I can see the logic. As far as I can tell, it simply needs tidying up. Here's my version. Since [imath]f_n[/imath] and [imath]f[/imath] are continuous, it follows that [imath]f_n-f[/imath] is continuous on [imath][a,b][/imath], and hence there exists [imath]x_0[/imath] such that [math]\sup_{x\in [a,b]} |f_n(x)-f(x)| = |f_n(x_0)-f(x_0)|[/math]. Then, [math]\lim_{n\to\infty} \sup_{x\in [a,b]} |f_n(x)-f(x)| = \lim_{t\to 0} \left| \frac{f(x_0+t) - f(x_0)}{t} - f'(x_0)\right| = 0[/math], so [imath]f_n[/imath] converges uniformly to [imath]f[/imath].

Usually they're informative. For example, people will often write something like [math]\underbrace{1+1+\dots+1}_{\text{n times}}[/math] which represents [math]\sum_{k=1}^n 1[/math] I find that it's a nice way of continuing steps in a proof without having to stop the train of thought, as it allows you to elaborate on a certain point in, say, a chain of equalities as is in your case.

Wow. I mean, I hate to break your bubble here but D H's post easily constitutes precisely what any sane mathematician would regard as a 'formal post'. I don't have much to add to Capn's and mooey's posts here other than I'd advise the experts to give your posts a very wide berth from this point forwards. It seems to me like you're less interested in learning mathematics than constantly starting arguments over trivial proofs such as these.

That clip was pretty funny All I know is that in the coming election, I'm not voting Labour. That's about as far as I've gotten. We don't really seem to have much choice between any of the three major parties, and my concern is this is just going to encourage the growth of rather nasty parties like the BNP and UKIP. What I want is a Government which keeps health, education and transport public. (By transport, I really mean infrastructure, not necessarily the operators of services on that infrastructure). I would like these things to be run in an efficient manner which doesn't waste public money. And I would like much more investment (again in an efficient manner and with proper oversight) into education. What I do not want is a Government which starts to intrude into the private lives of people in this country. For example I do not want: identity cards (but more specifically the national identity register); ContactPoint; many of the other massive (and useless) IT projects the government has put out there; massive expansion of police powers to stop and search, the Digital Economy Bill and so forth. I think that what I want is not too dissimilar from what most people want. I just wish someone would do it

Tacobell, in the first post, is your range supposed to be [math][0,2\pi][/math] instead of [math][0,2][/math]?

In the interval [0,2], I get a single turning point of [math]\pi/4[/math]. If you didn't get this, you should put your working up and see where you went wrong.

Yeah, I know what you mean. I'd buy one Merged post follows: Consecutive posts mergedOh and by the way, I voted for the integral. But I guess that was pretty obviously going to be my choice

triclino, the hint is not irrelevant. In fact it is a key step in the proof - the first step, in fact. Please refer to my other post regarding your behaviour.

No, this is standard notation. The floor function is [math]\lfloor x\rfloor[/math]. Plug it into the definition of uniform continuity and check that the definition is satisfied.

triclino, there are several members of the board (myself included) that know perfectly well what uniform continuity is - and indeed pretty much everything else you've posted about so far. I covered it myself about 6 years ago. I don't know whether you genuinely cannot answer your problem or simply wish to massage your ego by posting problems you already know the answer to. It doesn't really matter in any case - you need to make careful note of two things if you wish to remain a member of these boards: We are not here to answer your homework problems. If you have a proof already which you want checking, then post it. If you disagree with another member's point, then do so in a courteous fashion. As mooey has pointed out, it's totally unnecessary.

Looking good dude. I'm jealous - wish I had somewhere to fly rockets too

I think the more pressing matter is that of exoneration after the sentence is applied. Kinda hard to pull back someone from the dead, isn't it? For me, any other point either for or against the death penalty is immediately nullified by this one point alone. Whilst it's true you can't give someone thirty years of their life back, I would sure has hell rather give them the chance to start over than have their blood on my hands.