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The taylor series can be derived using the mean value theorem. \frac{f(a)-f(b)}{(a-b)} \approx f'(a) f(x) \approx f(b) +f'(x)(x-b) $ How do we prove the general taylor series using only the mean theorem? $

Thanks guys they finally fixed it but the tute I needed to get into is full so...

Re: HSC 2016 MX2 Combinatorics Marathon I never thought of doing it like that :O

Re: HSC 2016 MX2 Combinatorics Marathon It took me half a page.

Re: HSC 2016 MX2 Combinatorics Marathon We should leave this for new students. :)

Re: HSC 2016 4U Marathon - Advanced Level $ When will Newton's method converge and diverge if the inequality $ |\frac{f(x)f''(x)}{[f'(x)]^2}| <1 $ holds for all x $

Re: HSC 2016 4U Marathon - Advanced Level $ Find the polynomial, f(x), of $ (n-1)^{th} $ degree such that : $ f(x_1)=y_1 f(x_2)=y_2 ... f(x_n)=y_n $ Given that no two points have the same abscissas. $

LOL no one knew what to do... wasted 5 hours... and still not enrolled into my tutes... IT didn't know and the general people didn't know...

Well that escalated quickly...

Re: MX2 2016 Integration Marathon bump.

I think it is referring to the so called "sects" of Islam and how each interpret a verse. My friend gives school talks on bioethics but I myself am not to knowledgeable enough to provide positive help to you. Would you have any questions you'd like me to ask him?

Re: MX2 2016 Integration Marathon $ I'm not sure what you mean but my extension 2 teacher suggested this method: $ $ Writing in this order: $ u=... u'=... v'=... v=... $ You first multiply v diagonally and then vertically but the vertical one becomes a negative integral $ uv...

Re: MX2 2016 Integration Marathon New Question: \int_0^{\infty}{\frac{x \ln{x}}{(a^2+x^2)(a^2x^2+1)}}dx

Re: HSC 2016 3U Marathon Isn't this 2 unit? y'= \frac{-e^x}{1-e^x}

Re: HSC 2016 4U Marathon $ a) $ x= \frac{1}{1-\alpha} \alpha= \frac{x-1}{x} 0=(x+1)^{n+1} - x^{n+1} \frac{-b}{a} = \frac{\binom{n+1}{2}}{\binom{n+1}{1}}= \frac{n}{2}=S_n

1) Set up to parallel retort stands (separated slightly) with magnets attached to each with opposite polarities. 2) Connect either aluminium foil or a wire to an external circuit of 4-6 V and place inside the magnetic field observing the effects. 3) Vary the magnetic field strength by adding...

Re: MX2 2016 Integration Marathon The straight forward way is to just let u=\log{1-e^x} and the use IBP. But im guessing there's an easier way? Like reverse quotient rule +- a constant ?

Re: HSC 2016 MX2 Combinatorics Marathon $ If team is selected first $ \binom{n}{r} \cdot \binom{n-r}{1} $ If captain is selected first $ \binom{n}{1} \cdot \binom{n-1}{r} $ Taking note that the first and second methods give exactly the same value $ \binom{n}{0} \cdot \binom{n}{1} =...

Re: MX2 2016 Integration Marathon \int{\frac{x^4-x^2+1}{x^6+1} +\frac{x^2}{x^6+1}}dx \tan ^{-1}x + \frac{1}{3} \tan ^{-1} (x^3) +C

Re: MX2 2016 Integration Marathon $ Instead of using demoivre's theorem straight away that is : $ (rcis{\theta})^n= r^ncis{(n\theta)} $ He used binomial expansion and then used demoivre's theorem. $ $ You're allowed to do this because an even power removes the imaginary term and thus...