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Re: MX2 Integration Marathon Change tanx into sinx and cosx \int \frac{dx}{1+(tanx)^{\pi}} = \int \frac{(cos)^{\pi}}{(sinx)^{\pi}+ (cosx)^{\pi}}dx Then prove \int_0^a f(x)dx = \int_0^a f(a-x)dx and use it I = \int \frac{sin^{\pi}x}{sin^{\pi}x + cos^{\pi}x} Add both, I = x...

Re: MX2 Integration Marathon very nice!

Re: MX2 Integration Marathon Rationalise top \int \frac{1-x}{\sqrt{1 - x^2}} = \int \frac{1}{\sqrt{1-x^2}} - \int \frac{x}{\sqrt{1-x^2}} = sin^{-1}x + \sqrt{1-x^2} + C

Many times in year 8 and 9, I've always got the very first question wrong (like a simple factorisation or expanding question)

Re: MX2 Integration Marathon \int \frac{dx}{e^{\sin\left ( -x \right )}secx}

Sweet!

Re: HSC 2013 2U Marathon He 'completed the square'

Re: HSC 2013 4U Marathon nvm lol

ok cool

Show true for n=1, T_1 = 5 - 3 = 2 \rightarrow T_1 Show true for n=2, T_2 = 5^2 - 3^2 = 16 \rightarrow T_2 Hence true for n=1 and n=2 Assume true for n=k-1 and n=k i.e. T_{k-1} = 5^{k-1} -3^{k-1} \fbox{1} T_{k} = 5^{k} -3^{k} \fbox{2} Prove true for n=k+1, i.e. T_{k+1} = 5^{k+1} - 3^{k+1}...

ok

Ok very nice! Thanks for the help! Cleared up all the fog

Re: HSC 2013 2U Marathon Differentiate twice, equate to 0

Do I need to mention values of 'k'? Or just forget about all that? Because in the question, the recurrence relation is for n ≥3 and the thing im trying to prove is n≥1

Ok thanks! Do I need to discuss the values of 'k' for my assumption?

Ah i see.. Will I lose marks if I dont clearly write out: assume true for n=k-1? (for step 2) Can you assume n=k-1 when doing the n=k+1 step without saying that you assumed it?

Hi, can someone please check my WORKING OUT? $A sequence of numbers $T_n$ is given by $T_1 = 2, T_2 = 16$ and \\T_n = 8T_{n-1} - 15T_{n-2}$ $ for $n \geq 3 \\ \\ (i)$Use the method of M. induction to show that T_n = 5^n - 3^n$ $ for $n\geq1 This is what I did: Step 1: Show true for...

Re: HSC 2013 4U Marathon i've seen this somewhere...Cambridge 4U?

Re: Chess thread? Are you find with no time limit?

Re: HSC 2013 2U Marathon i am very sorry