HSC 2012 MX2 Marathon (archive) (2 Viewers)

cutemouse

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Re: 2012 HSC MX2 Marathon

Trebla likes his GP type of questions :p
 

largarithmic

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Re: 2012 HSC MX2 Marathon

Trebla's original question with limits 0 --> pi/2 was actually convergent. Just because a point is undefined, does not necessarily mean that the area is automatically infinite.
No its not...





Then as d approaches pi/2, cosd -> 0, and tand + secd -> positive infinity. So its pretty clear that the integral has to diverge
 
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math man

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Re: 2012 HSC MX2 Marathon

No its not...





Then as d approaches pi/2, cosd -> 0, and tand + secd -> positive infinity. So its pretty clear that the integral has to diverge
This does seem true, but e ing both
Sides then applying l hopitals rule
Will show this is actually convergent
As carrot said
 

seanieg89

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Re: 2012 HSC MX2 Marathon

Umm no, largarithmic is correct...the integral does not converge. The hypotheses of L'Hospitals rule are not even satisfied here.
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

Beforehand I was being lazy and checked the convergence using Wolfram (which claimed it converges and actually gave a value) instead of actually verifying it by hand.

Never again will I trust it for anything more than simple calculations ^^
 

AAEldar

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Re: 2012 HSC MX2 Marathon

I don't want to spoil the party but...

Any chance we could have questions more orientated towards a regular MX2 student, or a little harder, but something that most should at least be able to attempt. A lot of people would probably be scared off, especially since you guys are into or out of uni maths already!
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

I don't want to spoil the party but...

Any chance we could have questions more orientated towards a regular MX2 student, or a little harder, but something that most should at least be able to attempt. A lot of people would probably be scared off, especially since you guys are into or out of uni maths already!
Something I predict will appear in either the school Trials or the Complex Number exam term test (verified appeared in already 3 schools as per my prediction last year haha):

Find the value of:



OR

Find the value of:



Even better:

 
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nightweaver066

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Re: 2012 HSC MX2 Marathon

I don't want to spoil the party but...

Any chance we could have questions more orientated towards a regular MX2 student, or a little harder, but something that most should at least be able to attempt. A lot of people would probably be scared off, especially since you guys are into or out of uni maths already!
Should start at thread just for them elsewhere lol.
 

math man

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Re: 2012 HSC MX2 Marathon

Umm no, largarithmic is correct...the integral does not converge. The hypotheses of L'Hospitals rule are not even satisfied here.
yes, i simplied expression in terms of sin and cos, and got it down to ln|1/(1-sind)| so yes it diverges
 

math man

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Re: 2012 HSC MX2 Marathon

Something I predict will appear in either the school Trials or the Complex Number exam term test (verified appeared in already 3 schools as per my prediction last year haha):

Find the value of:



OR

Find the value of:



Even better:

come on so boring, (1) 2012 divisbe by 4 so 1, (2) collasping sum so boring, (3) AP with powers once you multiply them all.

I hope schools can take these and make them harder.

Combining these or putting in terms on n is a much better example as they would have to consider odd and even case
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

come on so boring, (1) 2012 divisbe by 4 so 1, (2) collasping sum so boring, (3) AP with powers once you multiply them all.

I hope schools can take these and make them harder.

Combining these or putting in terms on n is a much better example as they would have to consider odd and even case
Haha, the first one actually appeared in 3 school #1 assessment tasks already. Too predictable.
 

SpiralFlex

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Re: 2012 HSC MX2 Marathon

.......

Is there any chance my ranks will improve dramatically?
 

SpiralFlex

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Re: 2012 HSC MX2 Marathon

Shoe string fries. Perhaps you might want to stack them up and rotate it about the line y=4...

Maccas makes Spiral fat...
 

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