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Ok so for more 'complicated' single variable inequalities we should generally use calculus. Thanks for the help.

Yes, if Maths is one of your best subjects then you should do X2. Extension 1 pretty much becomes the '2 Unit' in Year 12. By that I mean its the exam where everyone in the grade gets 100%. And X2 has much more interesting questions (in the hsc).

KHCO3 can dissociate into K+ and HCO3-. K+ is a neutral ion. HCO3 exists in two different equilibrium H2CO3 + H20 <-> HCO3- + H3O+ (first ionisation of carbonic acid) HCO3- + H20 <-> CO3 2- + H3o+ (second ionisation) The equilibrium of the second ionisation lies very far to the left, so HCO3...

Consider the function f(x) = 3.sinx / (2 + cosx). Show that f(x) < x for x>0. This was Q16 from a 2012 trial paper, and the solutions used calculus (proof that derivative of x - f(x) is always positive). I was wondering if there was a non-calculus way to prove this. Something I came up with...

Wow thank you so much... I didn't even think about the AM-GM inequality.

Re: HSC 2014 4U Marathon These type of questions aren't even in the four unit syllabus are they? I mean I have no idea how to even to begin attempting this problem.

Prove that a/b +b/c +c/a is greater than or equal to 3, where a,b and c are positive numbers. Just can't figure out how to do this one. I also have a question about inequalities in general. When writing a proof, do we always have to start from a known statement and then reach the...

So i got a really bad teacher for eco this year who doesn't teach anything (they spent the entire week telling us what a 'want' is). So any tips going about learning eco by myself? I already purchased the market economy 2013 prelim. and excel prelim economics. And can anyone give tips on Eco...

I looked at the UNSW Medicine website and they recommend studying Chemistry. So no need to do Biology.