Search results

Re: MX2 Integration Marathon In this question we compute the Dirichlet integral using high school methods. $ 1. Show that: \\ \\$\int_0^{\pi/2} \frac{\sin((2n+1)x)}{\sin(x)}\, dx = \frac{\pi}{2}.$\\ \\ 2. Let: \\ \\$I_n:=\int_0^{\frac{(2n+1)\pi}{2}}\frac{\sin(x)}{x}\, dx$\\ and show that...

Re: MX2 Integration Marathon \int \sqrt[3]{\tan(x)}\, dx

Re: HSC 2014 4U Marathon $ $n$ lines are drawn in a plane, cutting it into regions. Prove that each of these regions can be coloured white or black such that no two adjacent regions have the same colour.$ Hint: Induction is one way to do this.

Re: HSC 2014 4U Marathon Perhaps the assumption should instead be: "Two opposite sides are equal and parallel."

Re: MX2 Integration Marathon Just to be clear, when you ask for an indefinite integral like this, do you want people to post a function whose derivative is equal to the integrand on some part of the real line or do you want a function whose derivative is equal to your integrand everywhere on...

A well known but nice practical question: You have a boiling cup of coffee (so 100 degrees) and you wish to drink it in exactly 5 minutes time. You like to dilute your coffee with milk (at say 5 degrees) in the ratio 1 part milk to 19 parts black coffee. You like your coffee to be as cool...

Re: MX2 Integration Marathon Bump. Also: \int \sqrt{\tan(x)} \, dx

Re: The Official Cricket Thread Is the reason their incredible streak of 14 away games without a win? (The most recent being a narrow win over the powerful West Indies mid 2011).

Re: HSC 2014 4U Marathon p=2 is not quite good enough to get second differentiability (consider f(x)=x^3/|x|, f(0)=0. this func is not twice diffble at 0, yet obeys the p=2 bound), (also, there is more than value of p that works).

I apologise for the sloppy texing. Hopefully it makes sense, but please point out anything that seems incorrect as typos are possible and the solution is my own.

Is anyone still working on this or should I post a solution today?

Updates: Yep, into a semi-regular routine. Am lifting larger quantities of metal than I used to be able to, although my fitness is not yet at where I would like it to be. Diet is also quite a bit healthier. Haven't spent much time on this but play more than I did at the end of last year so am...

I think that's what I got :).

Without latex rendering properly atm, I won't look carefully at your work yet realise...but something that might help all of you is a quick and dirty heuristic for why we should expect convergence: What is the probability of an arbitrary string of length m not containing n consecutive heads...

Re: The Official Cricket Thread It's not actually particularly high up on my list of favourite sports, I pretty much just watch the ashes. Had to watch at least a bit of this series after all the hype though.

I am not quite sure what you are doing in the calculation in your third case (if you cannot find any error in your reasoning then can you explain a little clearer please?), but that calculation shouldn't be so simple. After all, it's possible for things to happen like a string containing several...

Re: The Official Cricket Thread Yeah, you didn't miss out on too much.

Re: The Official Cricket Thread That's irrelevant to my point though, I am not saying our winning chances are better than theirs. I just think that a solid first innings from us doesn't look like it will leave enough time in the match for SAf to pile on a satisfactory lead and bowl us out on...

Re: The Official Cricket Thread What a dull pitch. Not ideal for a side trying to force it's way back into the series. Having had a good first day, if we can put up a solid first innings total then it should be pretty hard for us to lose this one, especially with SA lacking an specialist...

I will have a closer look at this soon, the approach was quite different to mine. No, nice just means that there is an aesthetically pleasing solution. The end answer is very simple but the problem isn't that easy.