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Re: HSC 2013 3U Marathon Thread I had a go at making a parabola question, its not as brute force as it looks. $The point$ \ P(2ap, ap^2) \ $lies on the parabola$ \ x^2=4ay $The tangent to$ \ P \ $is drawn and intersects with the parabola$ \ x^2=-4ay \ $at the points$ \ \ R \ $and$ \ S...

Re: MX2 Integration Marathon $Evaluate$ \lim_{n \to \infty} n \int_0^1 x^{n} \sqrt{x^2+1} \ dx (you may assume the limit converges)

Re: MX2 Integration Marathon Yep

Nothing too distinctive about him he is just a general right wing person, people just like picking on him because he's rich and its easy to sell that to the public

Re: The p00n thread Both parties are the same shit with different smell That's my opinion on the matter anyway

Re: The p00n thread That excuse only applies to economic policy, if the government forecasts a surplus and end up with a deficit due to some MASS change in economic condition then that is understandable. These people are politicians, they mostly have a background in law and economics and...

Re: HSC 2013 4U Marathon Yep that is the method that I had done. I did notice the binomial co-efficient in the middle but I'm afraid my permutations/combinations argument skills aren't very good so I couldn't do anything with it. Also you can tex in binomials using the \binom{}{} command...

Re: The p00n thread I agree that it is ethical and is only appropriate for media services to try and not provide a biased view, but they are their own enterprise and are very well within the right to do so. Murdoch is like a politician in this sense however, he speaks of free press and does...

Re: MX2 Integration Marathon That is incorrect Your answer should be positive anyway

Re: The p00n thread So its private companies which are supported by Rupert Murdoch not wanting to hold an advertisement that puts down Murdoch? A private news service is not obliged to give a completely objective news report(*), it doesn't make sense to expect unbiased political news from...

Re: The p00n thread Maybe people are frustrated that politicians literally lie to the public for votes, and this disheartens many people from discussing or wanting to know about politics. The stereotype that 'politics is a dirty game' is largely true and is another reason why many people don't...

Re: HSC 2013 4U Marathon $Using the squeeze theorem$ $i) Prove that$ \ \ \lim_{x \to \infty} \frac{\ln x}{x} = 0 $ii) Prove then that$ \lim_{n \to \infty} \frac{n}{\sqrt[n]{n!}} = e

Re: HSC 2013 4U Marathon Yeah that's what I was going for This inequality is a good one, it had me stumped for a while: $Show that$ \frac{1}{\sqrt{4n}} \leq \left(\frac{1}{2} \right ) \left(\frac{3}{4} \right ) \dots \left(\frac{2n-1}{2n} \right ) < \frac{1}{\sqrt{2n}}

Do the top 10 schools actually possess the top 10 teaching faculties (or something like that) or are their results due to how they attract the harder working students? I am leaning to the statement that its because of students mostly purely due to the high focus on information regurgitation...

Re: HSC 2013 3U Marathon Thread Yep that's pretty much it $Prove by mathematical induction for integer$ \ n\geq 2 \left( \frac{n+1}{2} \right)^n > n! Difficulty: Q14

Re: MX2 Integration Marathon Yep well done \int_{-\infty}^{\infty} \frac{dx}{(x^2+a^2)(x^2+b^2)}

Re: HSC 2013 2U Marathon $i) Sketch the line$ \ \ y=A-x \ \ $for$ \ x\geq 0 \ , \ y \geq 0 \ , \ A>0 $ii) The sum of 2 non-negative numbers is$ \ \ A \ \ $what is the maximum$ $ and the minimum value of the sum of the squares of these numbers$

Re: HSC 2013 3U Marathon Thread $Find$ \sum_{k=2}^n \frac{1}{\log_k u}

Re: MX2 Integration Marathon \int_0^{\frac{\pi}{2}} \sqrt{1 - \sin(2x)} \ dx

Re: HSC 2013 4U Marathon $Find$ \sum_{k=1}^n \frac{1}{k(k+1)(k+2)}