Dave

Fermat's Last Theorem.

Try calculating the first, second, third, fourth etc derivatives. You should be able to spot a pattern that can lead you to a general formula for the n'th derivative. From there, it's a simple matter of proving it via induction.

From myself and the rest of the staff at SFN, a very merry Christmas and a Happy New Year!

Well that just gives it all away

No, she couldn't. Teachers need to be protected as much as pupils do, and allegations of sexual advances or other such inappropriate behaviour can ruin careers. My mother and aunt are both teachers (of English) themselves and either one of them would do exactly the same thing in their situation. Does this make them 'bitches'? No; it makes them responsible teachers. No, I don't "see what you mean". As far as I can tell, you landed yourself in this mess, and are attempting to shift the blame from yourself to others. It is your own responsibility to get yourself out of this situation. If you really believe you are failing, then ask to be moved to another class. Incidentally, please do not use any further profanity in this thread. It's not necessary and, in any case, is against forum policy.

I'm sorry for the delay. Hopefully the site should be up sometime today, I just have to write a few documents.

A very merry Christmas to you all

I'd think it's (reasonably) safe to assume that your e-mails got through. Unless your PHP script took a completely unreasonable amount of time to finish, it's likely that apache would run the script until it had output, then die after it had found out the connection had dropped.

A better way of doing it (that avoids implicit differentiation) is to rewrite [math]x^x = e^{x \log x}[/math], and simply use the chain rule. CPL.Luke's way is the best I can think of for your limit and trig problems.

Your teacher is correct. Check through your calculation - there will probably be a silly error there somewhere

Yes, I think that's probably the best thing to say. I don't think that people would generally ask for one to do LU decomposition on a matrix by hand in exam conditions

Row-reduction is pretty much the only way of solving these.

Just before you read this, you should note that I particularly dislike the choose-one-or-the-other style questions. You can't boil down particularly complex issues (such as racism) to a simple case analysis question. Also, I'm hoping that Phi doesn't come after me with the beating stick for belittling his question I'm hopeful that most normal people would, in a relaxed environment such as this, say that they would just pick 'at random'. However, if this were to actually happen, then the last thing that you're going to be doing is thinking rationally. Just the time pressure alone and the amount of adrenaline rushing through your body would be enough to make the vast majority of people act solely on instinct. My point? It's not racism if a black guy goes for the black baby and a white guy goes for the white baby, as eloquently pointed out by SkepticLance. The only way to eradicate any racial bias from this problem is by letting them both die. That's a possibility that I hope most people would not even consider.

swansont, I totally agree with that and I believe that peer review is the only sensible way of doing any kind of science. On the other hand, a lot of these people aren't scientists, and aren't necessarily used to receiving the kind of formal criticism that most people are used to giving out on these issues. I'm not trying to cast blame on anybody here, rather just make some sort of observation. ajb, I agree that some of the issues on here could be solved by looking in the library or just googling. However, some people just aren't good book-readers and/or do not know where to look. I certainly think SFN serves a purpose, if only to point people in the right direction in some circumstances.

I think it's good that a lot of people have enthusiasm for science. To be honest, I really don't mind when people come up with the crackpot ideas, as long as they're prepared to receive the criticism and learn from where they've gone wrong. (Granted, in a lot of cases this doesn't happen, but it does from time to time). It's quite disheartening to see these guys being mauled by conventional scientists, as quite a lot of thought has probably gone into some of these ideas, and whilst they may not hold up, commendation should be given for the effort of going out there and thinking them up. I would like to think that it's not them being lazy, and rather that they don't have the time or experience to do so. As far as I can see, and drawing huge conclusions from my limited knowledge, there seem to be two main groups of these guys. Those who are teenagers, who are keen to go beyond their current knowledge of the subject to get to more interesting things that they haven't learnt yet, and adults who like to do science as a hobby (in whatever form). Hopefully the former should be able to learn where they were going wrong by progressing through the education system, and ideally the latter should realise by us pointing out mistakes. From my own experience, the last thing that people want to do after a hard day's work is sit down with some Analysis textbook or something and get stuck in to some juicy epsilon-delta arguments. Those are my two cents, for what they're worth.

Well, when we differentiate say, sin(x), we assume that x is given in terms of radians. If, on the other hand, x was given in terms of degrees, then the derivative we get would be: [math]\frac{d}{dx} \sin \left( \frac{\pi x}{180} \right) = \frac{\pi}{180} \cos \left( \frac{\pi x}{180} \right)[/math] This isn't a very nice function to be dealing with, so we only consider x as being done in terms of radians. Really, you should use radians exclusively over degrees, as they're a far more useful and natural way of describing the notion of an angle.

I do agree with this. I have the New Tab button right next to the Home button, and it comes in handy quite a lot. My main gripe with IE7's tabs is that they're so huge - I just want them to be nicely lined up, out the way without taking up a fair proportion of my viewing area.

I've tried IE7. I didn't like it at all, and went back to Firefox within about 30 minutes. Here's the major reasons: I like the fact that Firefox 2 supports both extensions and theme modifications out of the box. IE does not. The most useful plugin in the world, AdBlock, doesn't run under IE as far as I'm aware. Microsoft has shown us time and time again that they really don't care about standards. It's taken them 6 years to bring IE6 up to scratch, and only after immense complaints from the web development community. I would prefer to stick with Firefox, simply because I know that they will uphold these standards. I don't like the fact that I have no menus in IE 7. I don't like IE 7's implementation of tabs. The DOM inspector is possibly the most useful tool I've come across when debugging layouts. Don't get me wrong: IE7 is not a bad browser. However, I prefer to run Firefox 2, safe in the knowledge that it's much less likely to break my entire system.

I don't think I can add much to what's been said already, but even as a big fan of the show I agree with swansont. I certainly believe that the hosts and producers don't believe that they're going to categorically prove or disprove particular myths in a purely scientific fashion, simply because they don't have the time nor are properly trained scientists. My opinion is that it's a very good way of getting people interested in science, and definitely encourages a lot of kids to try and get involved - this is a good thing. Of course, the flip side of the coin is that they're not going to learn the proper scientific methods from the show, which is a bit unfortunate. However, I'm always impressed that they are completely willing to take what viewers have seen, re-do experiments and in some cases completely change their verdicts on previous work. Lots of kids (and adults) could learn a lot about this sort of attitude towards science.

Yes, it does depend on the processor. But temperatures around 100C are just not going to be good if run like that for long periods of time. It doesn't take a whole bunch of effort to cool your processor down effectively; if your current heatsink isn't doing a good enough job, then just buy another one and slap some Arctic Silver on there. Out of interest, which processor do you currently have in that machine, Callipygous?

Take great care when using degrees in integrals and other such calculations. It is a much better approach to use radians when dealing with this, and then convert the angle over to degrees afterwards. Trig functions tend to break easily when not handled under radians in terms of calculus.

Yes, you should be concerned about temperatures as high as 95C - they can cause permanent damage to your processor quite happily. You might want to consider whether you're using too much thermal paste; you only need a reasonably sized blob in the middle of the head spreader for it to do its job efficiently. Other than that, make sure the fan on your heatsink is not caked up with dust, or otherwise buy yourself a better heatsink.

Sorry, but you just have to show a little patience. I have an awful lot on my plate at the moment. I will try to get the plugin up today, but I can neither guarantee this nor offer any support if the plugin does come out.

I shouldn't worry about it. Most of the people I now know on the fourth year of a maths degree can't add up any more - I know I certainly can't

Well, firstly because it's clearly a function. It's not "higher math", rather a fact. It's given a special name since there's a whole load of things that you can do with the trigonometric functions that you just can't do with a lot of other functions. For example, Fourier series are completely reliant on the idea of expanding a function in terms of sines and cosines, and this is in turn immensely important in the field of partial differential equations. In the case of a calculator, I would imagine that there is certainly some sort of algorithm used. A Taylor expansion can give very accurate results within the range [math][-\pi, \pi][/math] using very few terms, and since sin is periodic, this seems to effectively solve the problem. However, I don't know for sure that this is the method that they use.