I know it might a bit late to ask, but please help >< (1 Viewer)

[CcYann]

this is the answers for 2007 4unit paper Q8 c) iii) & ii)
I have done ii)
my question is, for part iii) how can you think of changing the format of what you have got for ii) into this?
any help would be appreciated.

 

[CcYann]

anyone please?

 

[SpiralFlex]

I don't understand what you are asking

 

[SpiralFlex]

Do you mean how you change it into the form of the limit?

 

[wantingtoknow]

I guess what he's asking is how do you know you should change the solution of ii) into the equation in iii) first line

 

[SpiralFlex]

Whenever we have a limit, we may have to use our result sin x/x as x approaches 0. But as we can see, the limit involves as n approaches infinity. But we have no choice but to see what we can deduce if we can put it in that form.

That means we need two sets of pi/2n on the bottom. So we'll put that in first, I can move the n^2 in.




Note this is NOT our original expression, to compensate, times by pi^2/4,









Note as x approaches infinity for sin x/x , it would be zero right? However, we treat pi/2n as the "x" and the n separately. Let's let x = pi/2n, so we have,



Consider, x=pi/2n, as n approaches infinity, x diminishes and approach to zero.

 

[D94]

Sprial, s/he's not asking how to do it, I believe s/he's asking how do you realise that in the exam. Obviously now, it's blatantly obvious, but during an exam, it may not be, so s/he's asking what are the tell-tale signs that it can be split into a small angle approximation problem.

CcYann, you just do papers and you pick up tips along the way. But the main issue would be n*sin(c/n) (c is constant) as n approaches infinity, so you need to manipulate that expression so you don't have an indeterminate form.

 

[SpiralFlex]

Okay, i'll explain the thought process.

 

[CcYann]

yes,

I guess what he's asking is how do you know you should change the solution of ii) into the equation in iii) first line

 

[CcYann]

thank you all so much

 

[Mr Slick]

lol