HSC 2002 Q6bi) & ii) (1 Viewer)

[SkimDawg]

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2002exams/pdf_doc/mathemat_ext1_02.pdf

I was somewhat enjoying doing this paper until I got to this. Can someone show me how its done please. thanks.

 

[Zeber]

First of all, it is a stupid question to ask in a 3unit paper, at least in 4unit trials they give a diagram

Anyhow, draw the graph y = 1/x as neat as possible (we only need the first quadrant)

Label 1, n and n+1, and the inequality is achieved by considering the areas of the rectangles formed.

 

[shaon0]

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2002exams/pdf_doc/mathemat_ext1_02.pdf

I was somewhat enjoying doing this paper until I got to this. Can someone show me how its done please. thanks.

6bi)
When integrated.
1/n+1 < ln((n+1)/n) < 1/n [trying to prove this]
draw the y=1/x in the first quadrant only. try to form a rigid shape ie. rectangles or even squares.
This inequality will hold in these parameters (if satisfied) that is. Which it will be because your trying to prove this.

bii) manipulate the integrand i've given you and you should get the answer.
1/n+1 < ln((n+1)/n) < 1/n
HINT: use log laws and exponentials.

 

[SkimDawg]

First of all, it is a stupid question to ask in a 3unit paper, at least in 4unit trials they give a diagram

Yeah I agree. I've never seen something like this before, so at a first glance it was pretty much a mind blank.
Thanks Zeber and shaon0 for clearing things up.

 

[friction]

Hehe i just did this one. Anyone else think it was a pretty easy paper. Although i sat there looking at the last question for a bout 10 minutes not getting it till i realised the dots were times not points.