Help with HSC question (1 Viewer)

[fartman]

I know this is a bit late lol, but can someone help me with question 8 b) (v) in the 2004 HSC exam ? here's the link
http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2004exams/pdf_doc/maths_ext2_04.pdf
Thanks

 

[jennnnnnn]

u^n / 1+u^2 < u^n

integrate both sides from 0~1

LHS becomes In, which is less than [1/n+1 u^(n+1) ](bounds from 0~1) = 1/n+1

hence In < 1/n+1

since In is above the x axis except at u=0, then the area represented by In is positive In>0

thus 0 < In < 1/n+1

hence 0 < I2n < 1/2n+1

limit as n -> infinity for both sides and you get

0< lim n->inf I2n < 0


therefore lim n - > infinity I2n=0

lim n-> infinity (-1)^n I2n = 0

i.e lim n-> infinity Jn=0

 

[Nws m8]

u^n / 1+u^2 < u^n

integrate both sides from 0~1

LHS becomes In, which is less than [1/n+1 u^(n+1) ](bounds from 0~1) = 1/n+1

hence In < 1/n+1

since In is above the x axis except at u=0, then the area represented by In is positive In>0

thus 0 < In < 1/n+1

hence 0 < I2n < 1/2n+1

limit as n -> infinity for both sides and you get

0< lim n->inf I2n < 0


therefore lim n - > infinity I2n=0

lim n-> infinity (-1)^n I2n = 0

i.e lim n-> infinity Jn=0

She is the state ranker ! fahkkk hahaha

 

[fartman]

She is the state ranker ! fahkkk hahaha

Really? fuaaaaark
haha thanks so much jennnnnnn!

 

[fartman]

wait one sec, not sure if it matters but in the question it has less than or equal to signs? while u put less than signs?

 

[Nws m8]

Really? fuaaaaark
haha thanks so much jennnnnnn!

kidding