SpiralFlex
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HSC 2012 MX2 Marathon (archive) (1 Viewer)
- Thread starter nightweaver066
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SpiralFlex
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Re: 2012 HSC MX2 Marathon
^This is to make other students welcomed.
^This is to make other students welcomed.
SpiralFlex
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Re: 2012 HSC MX2 Marathon
Ewwww
Ewwww
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.Ewwww
SpiralFlex
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Re: 2012 HSC MX2 Marathon
Use da powerfwul serreees
Use da powerfwul serreees
SpiralFlex
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Re: 2012 HSC MX2 Marathon
Some Conics...
\; $Let$\; a\;$ and $\;b \;$ be positive constants.$)
\; $Consider the curve$ \; E_{1}: y=\sqrt{27-3x^2}, \; $where$ \; 0<x<3,\; $and the curve$\; E_{2}:y=\sqrt{9-\frac{x^2}{3}}\; $where$ \;0<x<3\sqrt{3})
 Find the point of intersection of \; $ \;E_{1} \; $and$ \; E_{2}\; \; \; \fbox{2})
 Let$ \; L\; $be the common tangent to $ \;E_{1} \; $and$ \; E_{2}\; \; \; )
.
 Find the equation of$\; L.\; \; \;\fbox{2})
 Find the area of the region bounded by $\;E_{1} \;, \; E_{2} \; $and$ \; L.\; \; \; \fbox{2})
Some Conics...
Nooblet94
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Re: 2012 HSC MX2 Marathon
For part alpha I can't work out why m<0. I can see it must be the case for the rest of the question because of the domain.Some Conics...
Re: 2012 HSC MX2 Marathon
Hmm I don't think I know enough on power series to get it
Carrotsticks
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Re: 2012 HSC MX2 Marathon
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.
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.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.
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.
largarithmic
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Re: 2012 HSC MX2 Marathon
uhhhhh... how can this be true? the right hand series (the harmonic series) diverges
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Re: 2012 HSC MX2 Marathon
3000th post!
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!
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