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Re: HSC 2013 2U Marathon no soln

Re: HSC 2013 2U Marathon You don't need to use that identity And your answer is correct, wel done

Re: HSC 2013 2U Marathon Did you try part (i) yet? ----- $Differentiate$ (x + \sin^2(e^x))^{4}

Re: HSC 2013 2U Marathon $i) Show that$ \frac{1-\cos^4 x}{\sin x \cos x + \cot x \cos^4 x} = \frac{\tan x \sec^2 x - \sin x \cos x}{\tan^2 x + \cos^2 x} $ii) Hence find$ \int_0^{\pi/4} \frac{1-\cos^4x}{\sin x \cos x + \cot x \cos^4 x } \ dx

Re: HSC 2013 4U Marathon For I, I'm getting: I(m,k,n) = \frac{k^n n!}{(m+1)(m+k+1)(m+2k+1) \dots (m+(n-1)k + 1)} \times \frac{1}{m + nk + 1} Which is a little different to yours The inequality is still wrong though my bad, it should be: \left( \frac{k}{m+(n-1)k + 1} \right)^n <...

Re: MX2 Integration Marathon Yea something like that well done

Re: MX2 Integration Marathon \int_0^1 \frac{x^{2012}}{1+x^2} \ dx

Re: MX2 Integration Marathon Yea, well done Alternatively: \int \frac{\sin^2 x}{\cos^2 x + \cot^2 x} \ dx = \int \frac{1+ \sin^4 x -1 }{\cos^2 x (1+\sin^2 x)} \ dx = \int \frac{1+ \sin^4 x}{\cos^2 x (1+\sin^2 x)} \ dx - \int \frac{1}{\cos^2 x (1+\sin^2 x)} \ dx = \int \frac{\sin^2...

Re: HSC 2013 4U Marathon So for a general polynomial Q(x), with a root A^{1/3} + A^{-1/3} , in order to 'ensure rationality', then Q(x) = p(x) R(x) p(x) = x^3 -3x + (A+1/A) R(x) being a rational polynomial, therefore any rational polynomial Q(x) that has A^{1/3} + A^{-1/3} as a root...

Re: HSC 2013 4U Marathon I'm not sure if this is what you're looking for: x = A^{1/3} + A^{-1/3} By cubing, then subbing x back in p(x) = x^3 - 3x - \left( A + \frac{1}{A} \right) = 0 \ \ $has root$ \ \ x=A^{1/3} + A^{-1/3} \ \ $with rational co-efficients$ Considering the graph of this...

I'm more nervous for this than for paper 2 tbh

Re: For those doing 'The Justice Game'.... or any other specifiable Module C texts... 200% screwed, I haven't read the book and didn't pay attention, other than Prisoner of Venda and Malcolm X The whole book was equivalent to horse feces, at least my belonging novel was alright

There was a bonus question! wthhhh I've pretty much memorised this anyway I thought everyone did lol?

Don't worry only your best 2 sections count =)

He isn't the one with a dick painted red and blue with white stars

**George Orwell 2/10

1. See if you can get a spare 2. Write on your exam paper: 'soz my calculator broke' 3. Then from then on, you take \pi = \frac{22}{7} e = 2 + \frac{1}{2} + \frac{1}{3} = \frac{17}{6} And you're set I hope you remember all of that stuff from primary =)

My writing is small, but I still write around the same as average but I end up using less pages, will the hsc markers think that I'm not writing that much or will they recognise that the lack of pages is due to size?

Re: HSC 2013 4U Marathon Yea that's right but I did it in a different way without using Riemann Sums