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Re: HSC 2013 4U Marathon Exactly as carrot has done lol. A similar thing proves Gregory's series for pi.

Re: HSC 2013 4U Marathon You can't really use indefinite integrals here, the value of an indefinite integral is a class of functions differing by a constant, it is NOT a number so we cannot make claims about its limit. (at least not the sort of claims you are trying for here). Try to derive a...

Re: HSC 2013 4U Marathon Yeah the other bound would be needed. I think it is about the same difficulty.

Re: HSC 2013 4U Marathon And it shouldn't be surprising. You have used information about the poly. to give you an equation d must satisfy. This does NOT mean that every solution of this equation is a valid value for d. This is an example of "if" vs "only if". (And also an illustration of...

Rezen's construction provides a counterexample for transcendental numbers too.

Re: HSC 2013 4U Marathon Just a point on nomenclature: the object in d) is called a formal power series, not a polynomial.

Re: HSC 2013 4U Marathon Lol such a roundabout way of showing that equation has another real sol.

Re: HSC 2013 4U Marathon Much easier than most of the questions I post here, but still quite a cool result. $Let $f(x)$ be a continuous function defined on the interval $-1\leq x \leq 1$ which satisfies $|f(x)|\leq 1.$\\ \\i) Prove that there exists an $-1\leq\alpha\leq 1$ with...

Medieval II: Total War. The Kingdoms Grand Campaign Mod is amazing.

Re: HSC 2013 4U Marathon Wanted a substitution that mapped the interval [0,1] to [0,1] so I could express I in terms of itself and some other terms. (ie I wanted to make a substitution but I didn't want the limits of integration to change.) This was the simplest rational function I could think...

$Because ``seeing that'' $\alpha^2+\beta^2 < 0$ is equivalent to both roots are non-real is fallacious.\\ A simple counter-example is $z^2+4z+5$. This polynomial has no real roots, yet $b^2-2ac=6>0.$ $

Re: HSC 2013 4U Marathon Evaluating the definite integral is well within the scope of MX2, the substitution x=\frac{1-u}{1+u} kills it.

I have: sennheiser hd598's for all round purposes. nice open and natural sound. unfortunately for this reason it also leaks sound both in and out. ultrasone 900's for a closed set which is absolutely amazing in the bass region. as a large chunk of my music taste lies in metal and electronic...

Re: Chess thread? Yep will make a standalone thread for it with web registration into the bracket.

Re: Chess thread? Okay, impromptu it is. Will organise the tournament on a weekend with much greater notice :). http://lichess.org/v222pzdm to anyone who wants to play me.

Re: Chess thread? Haha yeah, actually thinking about it do you guys just want to impromptu play each other tonight and save the tournament for another day more people are free?

Re: Chess thread? Matches will consist of two 10min a side games, one as white one as black. I will tell you who you are versing in your next match, you report the scores back to me as soon as you are done. Eg 1.5-0.5 would mean that first player won one game and the other game was a draw...

Re: Chess thread? Sweet, is Riproot here? Only one we are missing.

Re: Chess thread? Okay, make an account at lichess.org with username pretty similar to your BoS one so I know who is who. Will start this in about 10-15 mins.

Re: Chess thread? Cool, meet here 10ish.