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Re: First Year Uni Calculus Marathon Let\quad \beta \quad be\quad a\quad real\quad positive\quad real\quad numberLet\quad { a }_{ n }\quad be\quad a\quad sequence\quad of\quad positive\quad real\quad numbers\quad such\quad that:\\ \lim _{ n\xrightarrow { } \infty }{ \frac { 1 }{ { n }^{...

\left\lfloor \frac { 2017! }{ \sum _{ n=1 }^{ 2016 }{ n! } } \right\rfloor \\ =\left\lfloor \frac { 2017!+\sum _{ n=1 }^{ 2016 }{ n! } -\sum _{ n=1 }^{ 2016 }{ n! } }{ \sum _{ n=1 }^{ 2016 }{ n! } } \right\rfloor \\ =\left\lfloor \frac { \sum _{ n=1 }^{ 2017 }{ n! } }{ \sum _{ n=1 }^{ 2016 }{ n...

Re: HSC 2017 MX2 Integration Marathon Let\quad u=\frac { (k+1)x }{ x+k } \\ du=\frac { k(k+1)\quad dx }{ { (x+k) }^{ 2 } } \\ x=0,\quad u=0\\ x=1,\quad u=1\\ \frac { 1-x }{ x+k } =\frac { 1-u }{ k } \\ \frac { x }{ x+k } =\frac { u }{ k+1 } \\ \therefore \int _{ 0 }^{ 1 }{ \frac { { x }^{ a-1...

Re: Extracurricular Integration Marathon \int _{ 0 }^{ 1 }{ \frac { { \log^4{(x)} } }{ x+1 } dx }

\int _{ 0 }^{ 1 }{ \frac { { (lnx) }^{ 2 } }{ x+1 } dx }

Re: HSC 2017 MX2 Marathon we know that x^2+x+1=0. but this means that x is a cube root of unity ie x^3=1 therefore x^2016=1 and the solution is 2

Re: HSC 2017 MX2 Marathon Lagrange multipliers because why not

Re: HSC 2017 MX2 Marathon Yeh i wanted to put this in the advanced marathon, but none existed at the time it was posted so

Re: HSC 2017 MX2 Marathon I believe it's accessible to the extension 2 student so i put it on the marathon

Re: HSC 2017 MX2 Marathon IMO Longlist 1988

Re: HSC 2017 MX2 Marathon It's a surprise!

HSC 2017 MX2 Marathon ADVANCED A nice question

solve <a...

I got 2/3. take out the 1/9 and you get Sn as 1/9(1/4 x2/5x3/6...) the numerators and denominators of this cancel except for the first 1x2x3 and hence sn=1/9x6=2/3

Oh ok ty. Yeh i really dont want to solve odes in an exam

Yeh

Question: In general, are we allowed to be asked to be given the implicit derivative of a curve and be asked to sketch it in 4u? Ty.

Re: HSC 2017 4U Marathon here's a nice binomial followed by a harder binomial

please help. thanks

please help. thanks