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HSC 2012 MX2 Marathon (archive) (1 Viewer)

SpiralFlex

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Re: 2012 HSC MX2 Marathon

^This is to make other students welcomed.
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

Haha I didn't think about doing it that way, turns out was easier then I expected. Here's one that I can't do, let's see if one of you can figure it out.

The integral of this cannot be done via elementary methods. I was actually playing around with this very same integral when I was doing MATH1903. One night I was thinking "What will happen if I combine the mutually inverse functions e^x and ln(x) ? Will my math book explode?", so I started working on it.

Using Integration by Parts, we will acquire a very interesting integral:



The power series expansion for this is fascinating, as it involves the Euler-Mascheroni Constant (denoted by a Gamma).

This series can be found by acquiring the Taylor series for the function:



Then integrating the series term-by-term. iirc there is justification required for the convergence of the power series to the integral itself, but nothing too profound.

tl;dr can't do the question using HSC methods.
 

math man

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Re: 2012 HSC MX2 Marathon

pretty sure we will encounter this in complex analysis
 

IamBread

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Re: 2012 HSC MX2 Marathon

Ah okay, interesting... I have been trying to do this one for a while, never been able to get anywhere, now I know why :p.
 

Trebla

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Re: 2012 HSC MX2 Marathon

 
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Trebla

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Re: 2012 HSC MX2 Marathon

uhhhhh... how can this be true? the right hand series (the harmonic series) diverges
Woops, almost thought I stumbled on something neat there which was why it was modified in the first place. Ah wells, I'll stick to the original question



3000th post! :p
 
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