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  1. Paradoxica

    Predictions

    I doubt it. Difficult real world related rates questions (that stay within the scope of the syllabus) don't really exist. Trebla can vouch for this.
  2. Paradoxica

    Carrotsticks' Extension 2 HSC 2018 Solutions + Memes

    exposure to all of elementary mathematics will help but there are only so many hours in a human lifetime.
  3. Paradoxica

    Carrotsticks' Extension 2 HSC 2018 Solutions + Memes

    general expansion question xd idk
  4. Paradoxica

    Carrotsticks' Extension 2 HSC 2018 Solutions + Memes

    they've finally run out of idea so they just pulled a giant expansion question
  5. Paradoxica

    BoS Maths Trials 2018

    4U should be out tonight
  6. Paradoxica

    BoS Maths Trials 2018

    No. The case 0<b<1 can be transformed via a functional equation into the valid domain over where the result was proven to be true. Perhaps you should keep staring at the paper.
  7. Paradoxica

    BoS Maths Trials 2018

    The number of cards on the nth turn is n+2.
  8. Paradoxica

    BoS Maths Trials 2018

    what do you mean? you just replace n with k, they're just variables.
  9. Paradoxica

    BoS Maths Trials 2018

    I believe the correct question would be did anyone have a q16 to hand in at all. And we had less than half of them attempted.
  10. Paradoxica

    BoS Maths Trials 2018

    why everyone skip q16 ;_;
  11. Paradoxica

    BoS Maths Trials 2018

    The toilet of the second floor is comparable to USYD Carslaw
  12. Paradoxica

    BoS Maths Trials 2018

    We are aware of train delays, or own crew is affected by this, so you will not miss out on the start, please don’t be a no show
  13. Paradoxica

    MX2 Integration Marathon

    Re: HSC 2018 MX2 Integration Marathon The above question is literally impossible, in the sense there is no elementary closed form in terms of a finite combination of elementary operations and HSC-level constants.
  14. Paradoxica

    BOS trial

    whoosh was a joke my dude
  15. Paradoxica

    BOS trial

    ban
  16. Paradoxica

    Same Sex Marriage Debate

    It really isn't. Tolerating intolerance is never the answer.
  17. Paradoxica

    Higher Level Integration Marathon & Questions

    For all positive real numbers, the iteration derived from Newton's Method applied to the equation q(x)=x²-2 results in the f(x) described above, and converges to the positive real root of the equation. Hence, fn(x) converges to √ ̅2 for x>0 The point x=0 can be discarded, as it is a set of...
  18. Paradoxica

    Limit with binomial Coefficients

    slight overkill you can just use the thing i just posted with a riemann approximation to find the limit
  19. Paradoxica

    Limit with binomial Coefficients

    The first and last index terms can be discarded, since log(1) = 0 Rearrange the factorials to obtain: \lim_{n \to \infty} \frac{1}{n^2} \sum_{k=1}^{n-1} \log{\binom{n}{k}} = \lim_{n \to \infty} \frac{1}{n^2} \sum_{k=1}^{n} \log{ \left( k^{2k-n-1} \right) } From there, an integral...
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