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Re: HSC 2013 4U Marathon Oh right you said not real, yeah, then just take the complement.

Re: HSC 2013 4U Marathon What was your method that produced an incorrect answer?

Re: HSC 2013 4U Marathon |A|\geq 2

That's a pretty sweet track! I need to check out more of his stuff.

Definitely valid. I didn't go to tutoring, but competition with a mate was a large driving factor in high school maths.

Mathematical jokes are mandatory.

Re: HSC 2013 4U Marathon Perhaps this was a little difficult for a marathon question, although the needed tools are entirely within the HSC syllabus. I will post a solution a little later to illustrate how some different ideas in calculus interact.

Re: HSC 2013 4U Marathon Missing a factor of k!. Perhaps I should have given the form of the polynomial in my question but anyway, I think you should be able to prove the result if you know what the poly is.

a friend linked me to it ages ago.

http://www.youtube.com/watch?v=nrQZylE57y8 Not new but this was my favourite electronic track last year.

An elaboration of my post...

That's still just +1 ;).

Memorising formulae and procedures without understanding why they work and the scope of their applicability. The pragmatic reason why this is bad is that for questions that are even slightly different from those you have done before, you may be completely stumped because you cannot adapt the...

Re: HSC 2013 4U Marathon $Prove by induction or otherwise that a function $f:\mathbb{R}\rightarrow\mathbb{R}$ is $n$-times differentiable at $a\in\mathbb{R}$ if and only if there exists a polynomial $P$ of degree $n$ with: \\ \\ $\lim_{x\rightarrow a}\frac{f(x)-P(x-a)}{|x-a|^n}=0 \textrm{ and }...

If you are still making up your mind, the women and the pure mathematics courses are both generally better at usyd, should be a no-brainer :P.

Good to see some action.

Re: HSC 2013 4U Marathon 30. Fix the cube, count bijections from {1,2,3,4,5,6} to it's faces, then divide by the size of the symmetry group of the cube (because the first two steps count possible cubes with multiplicity).

Re: HSC 2013 4U Marathon Yep, once you learn things like the rigorous definitions of limits it will be much easier for you to determine if your manipulations are legit I promise.

Re: HSC 2013 4U Marathon Not quite, the fact that x^n\rightarrow 0 for |x|<1 is not quite enough. For example, if the thing we were multiplying x^n by in our integrand was something like 1/x^n, then obviously our integral would not tend to zero. The rest of the integrand is important too...

Re: HSC 2013 4U Marathon The error term is the integral, slight modifications to his working would make it legit and analogous to yours just with a sign change.