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HSC 2015 Maths Marathon (archive) (1 Viewer)

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Ekman

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Re: HSC 2015 2U Marathon

Im not in the position to solve it, due to other exams, but ill give you the integration formula:

 

Ekman

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Re: HSC 2015 2U Marathon

why the plus 2 at the end?
Whoops I just re-read the question, I didn't see that it was bounded between the x-axis as well. In that case there is no need for the +2
 

FrankXie

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photastic

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Re: HSC 2015 2U Marathon

My favourite logarithm question.

Differentiate (ln(ln(ln(lnx))))
 

InteGrand

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Re: HSC 2015 2U Marathon

My favourite logarithm question.

Differentiate (ln(ln(ln(lnx))))
Let , where the ln appears n times, , be denoted by . (Note that .)

By the chain rule, .

Carrying through with recursive formula for , we can find that , using at the end of the process.

Plugging in n = 4 gives us our desired derivative:

.
 
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Drsoccerball

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Re: HSC 2015 2U Marathon

Do you mean t's instead of x's? Otherwise we get infinite acceleration when the particle is at the origin.
damn it didnt see that when making it D: let me change the question too


 

InteGrand

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Re: HSC 2015 2U Marathon

damn it didnt see that when making it D: let me change the question too


You have to end up integrating logs to get x as a function of t, which is beyond 2U level.

This integral would probably be provided then if this question came up in 2U: .
 

Drsoccerball

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Re: HSC 2015 2U Marathon

You have to end up integrating logs to get x as a function of t, which is beyond 2U level.

This integral would probably be provided then if this question came up in 2U: .
I was thinking that they use the diagram to find the area so the integral isnt really needed
 

Ekman

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Re: HSC 2015 2U Marathon

I was thinking that they use the diagram to find the area so the integral isnt really needed
Sketching a diagram for is still beyond the scope of 2u...
 

Ekman

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Re: HSC 2015 2U Marathon

Draw them seperately
Also just to add, the question is a bit faulty as the displacement, velocity and acceleration is undefined at t=0. So when this particle starts moving, its initially location, velocity and acceleration is undefined... I understand that the question is asking about the integration between specific intervals, but in a mathematical and physical sense, the question seems a bit faulty.

Also drawing them out separately still wont help...
 
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