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Re: HSC 2013 2U Marathon \lim_{x\rightarrow 0} sinx \sin\left ( \frac{1}{x} \right )

Hey Carrot, can you please send me my rank? (if you are there...)

Are you sure its 2011 HSC?

Holy moly

Re: HSC 2013 2U Marathon my brain exploded sorry and yeh 'a' shouldn't be too nice

Re: HSC 2013 3U Marathon Thread Consider (1+x)^i (1+x)^j = (1+x)^{i+j} Equate co-eff of xm So.... \sum_{k=0}^m \binom{j}{k} \binom{i}{m-k} = \binom{i+j}{m}?

Re: HSC 2013 2U Marathon Remember that: T_n -T_{n-1} = d (this can be view differently) n=50 d = 249-233 = 16

Mine is Jet Li - industrial chemist

Re: HSC 2013 2U Marathon Whats the value of 'd'?

Re: MX2 Integration Marathon I give up now...please reveal your method

LOL!

Re: HSC 2013 2U Marathon \frac{1}{sinx} = cosecx \int cosecx * \frac{cotx - cosec x}{cotx - cosecx}dx = \int \frac{cosecxcotx - (cosecx)^2}{cotx - cosecx}dx \\\\ \\ \rightarrow = ln(cotx - cosec x) +C $as $\frac{d}{dx}\left ( cotx - cosecx \right ) = -(cosecx)^2 + cosecxcotx <------change...

Re: HSC 2013 2U Marathon Too hard lol But i do remember something...when integrating a cosecx, you multiply top and bottom by (csc^2 - cot^2) or (csc^2 + cot^2) or (csc + cot) or (csc - cot) then you use \int \frac{P'(x)}{P(x)}dx = ln[P(x)] +C

yeh and also concentration and focus play a huge role

Chem: electrochemistry, collaboration of scientists

Holy moly

I realised I made a mistake lol (check again, I edited my post)

Its an alternative way to long dividing - when the top degree of GREATER OR EQUAL TO bottom degree. Begin with: f(x) = \frac{x^3}{x^2 - 2x + 1} Write 'bottom on bottom' f(x) = \frac{x^2 - 2x + 1}{x^2 - 2x + 1} Do stuff to make it look like your true f(x) or else you've changed the question...

f(x) = \frac{x^3}{(1-x)^2} \\\\= \frac{x^3}{x^2 - 2x + 1} \\\\= \frac{x(x^2 - 2x +1)+2x^2 - x}{x^2 - 2x + 1} \\\\ = x + \frac{x^2 - 2x+1 +x^2 + x -1}{x^2 - 2x + 1} \\\\ =x+1 + \frac{x^2 +x - 1}{x^2 - 2x +1} \\ \\ = x+1 + \frac{x^2 - 2x + 1 + 3x -2}{x^2 - 2x + 1} \\\\ = x+1 + 1 +...

Re: MX2 Integration Marathon ahh, i see ze double angle...