HSC 2016 Maths Marathon (archive) (1 Viewer)

[Paradoxica]

Re: HSC 2016 2U Marathon

how do you simplify [cuberoot(x+h)-cuberoot(x)]/h lelel

Difference of two cubes

 

[leehuan]

Re: HSC 2016 2U Marathon

how do you simplify [cuberoot(x+h)-cuberoot(x)]/h lelel

What Paradoxica said.

Spoiler

Forget about rationalising the denominator and rationalise the numerator instead. You should've been taught how to find d/dx √x using first principles as well

 

[Nailgun]

Re: HSC 2016 2U Marathon

Difference of two cubes

does that work for cube roots?
wot

 

[KingOfActing]

Re: HSC 2016 2U Marathon

does that work for cube roots?
wot

Write out the difference of cubes x^3 - y^3, then after factoring let x = a^(1/3) and y = b^(1/3), see what you get

 

[DatAtarLyfe]

HSC 2016 2U Marathon

Ignore this

 

[porcupinetree]

Re: HSC 2016 2U Marathon

Instructive question

how do you simplify [cuberoot(x+h)-cuberoot(x)]/h lelel

 

[leehuan]

Re: HSC 2016 2U Marathon

Tfw this guy who already got into USyd is doing a 2U qn for Nailgun

 

[Nailgun]

Re: HSC 2016 2U Marathon

Write out the difference of cubes x^3 - y^3, then after factoring let x = a^(1/3) and y = b^(1/3), see what you get

Ahhh, I see now. That's pree neat, thank you.

I would never of thought of that lel

 

[porcupinetree]

Re: HSC 2016 2U Marathon

Ahhh, I see now. That's pree neat, thank you.

I would never of thought of that lel

(Side note: to be more rigorous, I should have validated my move from my 5th line to my 6th line by proving that each term in the denominator of the 5th line is continuous. But ceebs.)

 

[KingOfActing]

Re: HSC 2016 2U Marathon

(Side note: to be more rigorous, I should have validated my move from my 5th line to my 6th line by proving that each term in the denominator of the 5th line is continuous. But ceebs.)

Nah mate, epsilon-delta the whole proof

 

[Paradoxica]

Re: HSC 2016 2U Marathon

must also include 1000 page proof of foundations


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[leehuan]

Re: HSC 2016 2U Marathon

Nah mate, epsilon-delta the whole proof

Go home, you're drunk.

 

[porcupinetree]

Re: HSC 2016 2U Marathon

Nah mate, epsilon-delta the whole proof

must also include 1000 page proof of foundations


Sent from my iPhone using Tapatalk

Literally Paradoxica in his HSC exam when he has 2h 50min free because he does every other question by inspection within 10 minutes

 

[KingOfActing]

Re: HSC 2016 2U Marathon

Literally Paradoxica in his HSC exam when he has 2h 50min free because he does every other question by inspection within 10 minutes

derive every result by starting with the peano axioms

 

[si2136]

Re: HSC 2016 2U Marathon

derive every result by starting with the peano axioms

Mate 2 + 2 = 4 is an axiom

 

[leehuan]

Re: HSC 2016 2U Marathon

You guys are all drunk. This is a 2u marathon.

 

[InteGrand]

Re: HSC 2016 2U Marathon

Mate 2 + 2 = 4 is an axiom

There's like a 300+ page proof of 1 + 1 = 2.

 

[si2136]

Re: HSC 2016 2U Marathon

There's like a 300+ page proof of 1 + 1 = 2.

Yes ik

But people don't write the proof down do they

 

[Nailgun]

Re: HSC 2016 2U Marathon

"If you wish to make an apple pie from scratch, you must first invent the universe."
- Carl Sagan

 

[porcupinetree]

Re: HSC 2016 2U Marathon

You guys are all drunk. This is a 2u marathon.

"If you wish to make an apple pie from scratch, you must first invent the universe."
- Carl Sagan

3 deep 5 me