Dave

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.

If i were to prove that your proof is not correct we will have to formally analyze it

 

But can you formally analyze your own proof??

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.

I have to say, by far, the coolest t-shirt would be the biohazard. It's one I would wear without feeling like a pretentious intellect. It doesn't say, "look at me, I'm smarter than you." It's more of a declaration. "I like to take risks."

Yeah, I know what you mean. I'd buy one

Merged post follows:

Oh 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.

You mixing up ceiling function with the floor function.

No, this is standard notation. The floor function is [math]\lfloor x\rfloor[/math].

But according to what axiom or theorem you came to the conclusion :

 

[math]N=\lceil 1/(4\epsilon^2)\rceil+1[/math] or [math]N=\lceil 1/(4\epsilon^2)\rceil[/math]

Plug it into the definition of uniform continuity and check that the definition is satisfied.

Yes you can escape by writing nonsenses because the moderators of this forum

 

perhaps are not capable of detecting such unfounded mathematical nonsenses that you keep on writing.

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

You can revoke a death sentence by canceling it before it gets applied. In this case, the death sentence is fully revoked -- unlike a prison sentence, where only a portion of it can be revoked.

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.

That comment is valid if, and only if, the net effect of the immigrants upon the economy, welfare and culture of the country is negative. That has not been demonstrated.

Probably because the effects of such a mass-immigration policy are seen very much in the long-term scale. let alone after a policy of mass-immigration. Let me elaborate on that point.

In my mind at least, such a massive influx of people into the country is by not means a bad thing. However, unless they have both have a skill-set which is required in the country, and a willingness to integrate into the existing culture of the country, then this inevitably leads to an overpopulated, undereducated country which in 30 or so years is going to be under intense pressure to provide social support for these people when they retire. Given the advances in medicine and rise of the average life expectancy after work, the UK was pretty poorly placed to deal with the average population ten years ago; now we have a much larger gap to contend with.

Alongside this is the damage created by allowing people into the country who do not intend to try and integrate themselves into the culture, and the resulting racial tensions incited from it. From my personal experience of living in a migrant-rich area for pretty much my entire life, allowing new migrants in has essentially encouraged compartmentalisation of communities with different ethnicities. So, the UK is really only multi-cultural in the sense that people of different cultures all occupy the same landmass; as far as I can tell, there is very little in terms of interaction between them. To see the effect this is causing, take a look at some organisations such as the BNP or Islam4UK.

The thrust of this thread that is marginally more convincing is the alleged lie told by the labour government. However, even there I see no proof that the motivation was as described. Moreover, I am automatically skeptical about ascribing single motives to complex political actions. Such simplification is rarely accurate or meaningful.

The current government has, to all intents and purposes, confirmed (albeit implicitly) they were in the wrong by allowing this immigration policy by subsequently implementing a Canada-esque points based system in the last year or so. There are two main questions I'd like answering:

• Why edit the public report and only release the unedited version (with a much higher emphasis on social engineering) upon a Freedom of Information request?
  
• Why have such a policy in the first place? Canada's system has been around for a long time, and seems to be attracting good skilled labour to the country.
  

I would think that the damage would be from the lying itself, not from the result of the policy. You don't lie about immigration in a democracy. That's a whole order of political magnitude beyond a "third rail", at least on the domestic scale.

My own personal opinion on the 'damage' side of things is above. The truth is at this point we don't really know what will happen. My post is only speculation based on what I've read and what I think about it.

In terms of the political damage, I imagine nobody will really pay much attention to it, and/or it will be buried by the spin doctors. The Labour government seems to be pretty good at spinning their way out of stuff at the moment, Teflon Tony included. Hopefully that will come to an end come May

Jeez, that looks like a pretty nasty equation. I doubt you're easily going to find any solutions via standard methods.

You're looking for something like spherical polar co-ordinates.