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It's not a function, so you can't apply L'Hopital (unless you want trivial results)

Not really, it's the standard convention to mark the end of a proof, which appears everywhere in mathematical papers. I have yet to see one academic who does not use it or some symbol to denote end of proof in a proper document. The default end of proof symbol in LaTeX is a box, although that...

1.1, or 1.0999... What is 0.000...1? If we do allow the use of infinite zeroes before the one (which is technically invalid), we obtain it as (lim n->inf (1/10)^n), which is zero.

Surely there are engineering streams with lower UAI than even straight science that you can get started in and transfer to your desired stream after a year?

Re: When do exam timetables come online? Known it for a while (internal exams), only one real exam on Tuesday 18th, one take home during stuvac.

(i) The probability that Anne picks the black jelly bean is the sum of her picking it up on the first go, her second go, etc. First go: 1/n Second go: (n-1)/n*(n-2)/(n-1)*1/(n-2)=1/n (first two fractions are Anne and Bruce pick up white) Third go...

School paid for AMC so cost was never an issue.

Considering that an emeritus professor who came up with the HSC/UAI scaling system also agree that the statistics taught in high school actually works against uni statistics and that it should be left to university to teach statistics, I would say that has much weight.

If your marks are good you can get that requirement waived. I would trust a statistician who has done BSc(Adv Maths) over an actuarian in terms of statistics. The actuarian has more market knowledge, but that's much easier to learn than statistics.

Why does graduating under BSc (Adv Maths) require you to stay back an extra semester?

Absolute intelligence has nothing to do with UAI. It simply means that in any other year, you would have received a higher UAI. Even suppose you have an IQ of 200, but you were with a bright cohort and only get a UAI of 99. Would you still apply for USyd law (ref 99.55)? Probably not. The...

Whether a year is smart or not should not reflect on the cutoff, considering UAI is a ranking and even in a 'smart' year, people will still come first, second, third etc. A inflated cut off from 2008 would only imply a larger candidature who undertook the HSC, as spots are generally fixed and a...

TSP units are worth as much as you can convince them it's worth. You can get away with doing projects requiring little work. There has been SSP classes which require only an hour or so of work for 3cp for the whole semester. I wouldn't recommend 60cp in a year. If you think you are incredibly...

It should be defined for all real x It's odd, so just rotate that bit to the negative half.

In its current scope, no. Critical analysis of texts learnt in English is not vital in later life unless you are looking at one of few specific fields, and I would prefer reasoning to be learnt through the sciences and maths instead. There are many people who lack reasoning and numeracy skills...

If we're going to be completely rigorous here, the last line doesn't follow from the above, since then you are assuming 1!=1 and that n! is defined to be n(n-1)! even for n=1.

Agree with the posts on taking up a quantitative major. Unless you want to continue with research in your field, BSc is not about the knowledge you learn during uni, but rather the problem solving and logical deduction skills you pick up in your degree in science. This opens up a wide range...

Break the integral into 2 and |x|, and use the fact |x| is even

I don't know your ability, but I would recommend not to overload if possible. The prospect of finishing early simply isn't worth it. And doing eight subjects in a single semester is not fun.

How is the olympiad a spectator sport? It is purely a tournament for the brightest high school students to strive for excellence.