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Re: HSC 2013 4U Marathon Lol sledgehammer :P.

For Q3 here is my approach: $Observe that:\\ $2^{3^n}+1=(2^{3^{n-1}}+1)(2^{2\cdot 3^{n-1}}-2^{3^{n-1}}+1).$\\ \\Using this identity recursively establishes that $3$ divides $2^{3^n}+1$ for every non-negative integer n.\\So now fix $n\geq 1$ (the case $n=0$ is trivial) and let $l$ be the...

if they allowed you to take it home I am sure its okay :).

What were the questions like?

Yeah, I've heard that from a few people.

Yeah man, I was never that good at it but its got such an amazing feel to it. BoS game sometime.

Finally bought Starcraft II: WoL+HotS. On first impression it doesn't feel as amazing as brood war did (despite the immense technical improvements, many of which make essential actions less tedious) but it is growing on me.

Re: HSC 2013 3U Marathon Thread The key isn't that the integrand tends to zero, we need the whole integral to tend to zero. (Unless we have more sophisticated tools at our disposal for going from the former to the latter.)

Its too hard for me to order them and I am probably forgetting some but here goes: Frou Frou- Details Parkway Drive- Horizons Emery- In shallow seas we sail Avalanches- Since I left you Buckethead- Electric tears. I really want to put Placebo- Meds and August Burns Red- Constellations in there...

Have been enjoying RTS's a lot recently although I am terrible at them. Mostly sc:bw, aoe2:FE, bfme2:rotwk with the 2.02 balance patch (original is heavily unbalanced but when patched this game is crazy fun and much easier to play than bw/aoe2).

Personally I italicise all of them.

You are a neoliberal Democrat. 6 percent of the test participators are in the same category and 56 percent are more extremist than you. More or less what I expected, pretty left leaning. I was pretty conflicted about some of the economic/military issues though.

If you really want to explicitly find such a curve which gives you a finite nonzero limit the key is that the singular behaviour is on the line y=x, so something like y=x^2+x will do. No point on such a singular line can ever be a point of continuity though.

along y=2x the second term simplifies to -4x, which does indeed tend to 0. x^3/(1-x) also tends to 0, not negative infinity. x/(x-sqrt(x)) also tends to 0, not 1.

Re: MX2 Integration Marathon Pretty much, I would prefer if you did the work to show the epsilon term tends to zero, this is not too hard. Also it is probably better to describe your slices as being perpendicular to the y-axis (rather than the x-y plane), ie every point in a slice has the...

1. Looking at the line y=x is enough. 2. Use the definition of partial derivatives and Taylor's theorem in the form f(x+h)=f(x)+hf'(x)+h^2f''(x)/2+O(h^3).

Re: MX2 Integration Marathon The following question is set in http://en.wikipedia.org/wiki/Three-dimensional_space with the standard coordinates. $Let $r>0$. \\Define $C(r)$ to be the solid of revolution formed by rotating the planar region $\{(x,0,z)\in\mathbb{R}^3:|x|\leq r,0\leq z \leq...

Re: HSC 2013 4U Marathon Its important to note that this idea only works here because the series he is presumably working from (the arctan Maclaurin series evaluated at 1) is alternating. This generally would not be a valid way of bounding the error term of series.

Re: MX2 Integration Marathon Pretty sure no elementary primitive exists. Can people please be more careful when posting questions?

So where do you draw this line? Is alcohol acceptable? Are prescription drugs acceptable? Is Panadol acceptable? Are research chemicals in a legal grey area acceptable? What is the issue here, legality of the substance in question or potential to damage the body?