I want inequality questons (2 Viewers)

[freaking_out]

Originally posted by turtle_2468
no chance that'll appear either
You know hard?
Well, this q is around 5 degrees above it.
If you REALLY want the proof, pm me and I'll give it to you...
That's what they say every year btw... that it's going to be extra hard... but the point of the paper is to distinguish the candidates anyway, so they can't really make anything except q8 that much harder
and... who cares? The point is to get the best ranking possible right... so if there's an ultra hard q that u can't do, it's ok as long as others can't do it either!

u c, if these questions are "possible" for a question 8, and then i learn how to do it, (and if by luck its in the test) then i have a remarkable advantage over the kids in the state.

yeah, anyway about riemens hypothesis, apparently drbuchanan taught it to all of his 4u students, coz he really thinks its gonna b in the test. so yeah, thats why, just post up stuff on it so i can learn.

 

[turtle_2468]

ok. I think you know, but making sure... this question is NOT possible for q8. Seriously...
although, if you wanted to study something extra, go study the proof of AM-GM inequality. That has more chance than this... but not much still..

 

[Rahul]

hey turtle, what other things may be possible for these harder questions?
i know i may be stretching it a bit, but u mentioned one....

 

[freaking_out]

Originally posted by Rahul
hey turtle, what other things may be possible for these harder questions?
i know i may be stretching it a bit, but u mentioned one....

yeah, i wanna know as well....c we r not smart so we can only get marks in question 8 if we've seen the question bfore...

btw, how did u get two post counts rahul?

 

[Lazarus]

Originally posted by freaking_out
btw, how did u get two post counts rahul?

hahaha clever!

 

[Rahul]

Originally posted by freaking_out
btw, how did u get two post counts rahul?

What? you must be 'imagining' things....

turtle, could you direct me to a proof of the am-gm inequality which you feel explains it the best. there are a few on google, but i am not sure which one explains it the best.....thanks

 

[freaking_out]

Originally posted by Rahul
What? you must be 'imagining' things....

hmm....it must b the hsc stress.

 

[turtle_2468]

AM-GM:
very tricky and cat-out-of-hat proof from http://members.tripod.com/~spssmaths/in_3_notes.htm
The way I'd expect ppl to ask it in the HSC, if they ever were to do it, would be to do it step by step.
1) prove for 2
2) prove for k=2^q (ie only for cases where the number of terms is a power of 2)
3) substitute a_n=(sum of a_i, i from 1 to (n-1))/n-1 ie the average of all the others to prove it for k=2^q-1
4) use 3) repeatedly to prove it for lower powers.

How this would work for specific case like n=6:
you prove n=2 (easy), then n=4, then n=8, then n=7, then n=6. You don't actually do this anywhere in the proof, just showing how the above steps show it for all the numbers

 

[turtle_2468]

Other topics? One that I've always found tricky is firing a projectile into a sloped surface (ie where the projectile intersects with a st line, y=mx), do u know that one?

 

[enak]

For the AM-GM inequality, can't we just assume that? Or am I thinking about the Cauchy inequality (a1+a2+a3+...+an)/n >=nroot(a1a2a3...an) ?

Are you serious we have to prove that in the exam?

 

[freaking_out]

Originally posted by enak
....Are you serious we have to prove that in the exam?

well DUH!!!

 

[Rahul]

Originally posted by turtle_2468
Other topics? One that I've always found tricky is firing a projectile into a sloped surface (ie where the projectile intersects with a st line, y=mx), do u know that one?

no i havent, but i have seen where two parabolic paths intersect, but i think that is standard 4u projectile motion.

edit: for other possible topics, i have come across a couple, Cauchy Schwartz Inequality and Arithmetic Triangle Inequality. are they worth looking at, or are they outside the scope of 4u?

 

[ND]

Originally posted by turtle_2468

The way I'd expect ppl to ask it in the HSC, if they ever were to do it, would be to do it step by step.

I think they've done AM >= GM. I'm pretty sure I remember it from a past paper, i'll check tomorrow.

 

[freaking_out]

Originally posted by ND
I think they've done AM >= GM. I'm pretty sure I remember it from a past paper, i'll check tomorrow.

 

[Rahul]

yes i am thinking the same....

 

[freaking_out]

Originally posted by Rahul
yes i am thinking the same....

yep, ur in the "no chance in Q.8" boat.

 

[Rahul]

yes, unless i luckily read the proof to the question early on...

which is what i am trying to do

 

[freaking_out]

Originally posted by Rahul
yes, unless i luckily read the proof to the question early on...

which is what i am trying to do

yep true....its a bit like taking a stab in the dark.

 

[turtle_2468]

Okay...
you DON'T have to prove it in the exam. At least it's very very unlikely...

enak: The inequality you wrote down it the AM-GM. Cauchy is something else altogether.

Rahul: I think the q is in cambridge somewhere. Try it, it's nice Or I foudn it SOMEWHERE.. maybe HSC past q's? anyway. Cauchy schwarz is WAY out of the HSC syllabus, nothing you ever do in 4U will involve it. Arithmetic triangle, however, I think is part of the standard syllabus for harder 3U. Check in cambridge again...

Hmm. If I don't come up with any more, as I'm quite busy next few days, send me a PM around thursday and I'll think of a few...

 

[ND]

Originally posted by turtle_2468

Rahul: I think the q is in cambridge somewhere. Try it, it's nice Or I foudn it SOMEWHERE.. maybe HSC past q's? anyway.

Are you referring to the projectile and line type q.? There is one of those in a 3u past paper.