Recurrence relation qn - Singapore Forums by SGClub.com
Singapore Forums by SGClub.com
Sitemap Contact Us FAQ Singapore Forums by SGClub.com
Home Photos Member List Register Mark Forums Read  
Go Back Home > Lifestyle > School Life > Math Help » Recurrence relation qn

Why aren't you a member of SGClub.com yet??

» Join 130,000+ other members in chatting.
» Make lots of new friends here.
» Keep up-to-date with current events.
» Participate in Club outings.
» Download lots of Free Stuff!

Registration just takes 2mins and is absolutely free so join our community today!

I Want to Choose my Own Personal Nickname Now!


Reply
 
LinkBack Thread Tools Display Modes
Old 7th October 2012, 08:11 PM   #1 (permalink)
Experienced SGClubber
.Memo will become famous soon enough

 
.Memo's Avatar
 
Posts: 1,601
Join Date: Nov 2010
Likes: 10
Liked 23 Times in 22 Posts
Gender:

Recurrence relation qn

Q8iii)

Sponsors:
__________________
Back in action
.Memo is offline  
Add to .Memo's Reputation Reply With Quote
Old 7th October 2012, 10:33 PM   #2 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: Recurrence relation qn

x_n>ℓ → x_n - ℓ>0 → [x_(n+1)]² - ℓ²>0 → [x_(n+1)]²>ℓ²
x_n>ℓ → x_n>0 → x_(n+1)>0
Since both x_(n+1) and ℓ are positive, [x_(n+1)]²>ℓ² → x_(n+1)>ℓ

[x_(n+1)]² - ℓ² = x_n - ℓ
(x_(n+1) + ℓ)(x_(n+1) - ℓ) = x_n - ℓ
Since x_(n+1)>ℓ → x_(n+1) + ℓ > 1,
x_n - ℓ > x_(n+1) - ℓ
x_n > x_(n+1)

∴x_n > x_(n+1) > ℓ

I've not learnt JC math, so idk if there's a shorter way

__________________
Are you ready to get serious?
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 7th October 2012, 10:36 PM   #3 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: Recurrence relation qn

According to the relation:

Suppose Xn>T (no symbol to denote nicely, so just make do. )

(X(n+1))² - T² = Xn - T

Xn - T > 0, as Xn>T

(X(n+1))² - T² > 0
X(n+1) > T


Seperately, taking the same statement Xn>T, rearranging the statement:
(X(n+1))² - T² = Xn - T
(X(n+1))² - (Xn - T) = T²
(X(n+1))² - 0 < (Xn)²
X(n+1) < Xn

Hence, T < X(n+1) < Xn

(My solution will get the marks, however it may lack some explanations as it is difficult to explain inequality logics. )

__________________
Currently just a wanderer...
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 7th October 2012, 10:53 PM   #4 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: Recurrence relation qn

Originally Posted by Tetrahedron View Post
According to the relation:

Suppose Xn>T (no symbol to denote nicely, so just make do. )

(X(n+1))² - T² = Xn - T

Xn - T > 0, as Xn>T

(X(n+1))² - T² > 0
X(n+1) > T


Seperately, taking the same statement Xn>T, rearranging the statement:
(X(n+1))² - T² = Xn - T
(X(n+1))² - (Xn - T) = T²
(X(n+1))² - (Xn - T) < Xn²
(X(n+1))² < (Xn)² ∵ Xn - T > 0
X(n+1) < Xn

Hence, T < X(n+1) < Xn

(My solution will get the marks, however it may lack some explanations as it is difficult to explain inequality logics. )
It was difficult for me to see the in-between steps...

__________________
Are you ready to get serious?

Last edited by Betakuwe; 7th October 2012 at 11:00 PM.
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 7th October 2012, 11:39 PM   #5 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: Recurrence relation qn

Originally Posted by Betakuwe View Post
It was difficult for me to see the in-between steps...
Yes, thank you very much for completing the workings for me. Kinda hard to make a dummy solution for such a question.

Oh and your method works too, just that it works based on a different approach.

Generally, for inequalities question, change all inequalities to something with regards to 0 and 1. Makes things much easier.

__________________
Currently just a wanderer...

Last edited by Tetrahedron; 7th October 2012 at 11:43 PM.
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 7th October 2012, 11:53 PM   #6 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: Recurrence relation qn

Originally Posted by Tetrahedron View Post
Generally, for inequalities question, change all inequalities to something with regards to 0 and 1. Makes things much easier.
Heh, having worked with maths olympiad questions, inequality questions are extremely popular in maths olympiad and they are always so damn tricky and are my Achilles' heels

Here's a challenge:

__________________
Are you ready to get serious?

Last edited by Betakuwe; 8th October 2012 at 12:10 AM.
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 8th October 2012, 06:38 AM   #7 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:


More or less knew the solutions. Will type it out when I get home.

Sent from my GT-P6200 using Tapatalk 2

EDIT:

As |cos2x|<1
(sinx - cosx)/(cos2x) >_ sinx - cosx

|sinx + cosx - (sinx - cosx)/(cos2x)| >_ |sinx + cosx - sinx - cosx| = |2cosx| = 2 (Shown)

__________________
Currently just a wanderer...

Last edited by Tetrahedron; 8th October 2012 at 05:08 PM.
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 19th October 2012, 09:43 AM   #8 (permalink)
New SGClubber
danielync is on a distinguished road

 
Posts: 1
Join Date: Oct 2012
Likes: 0
Liked 0 Times in 0 Posts
Gender:

Re: Recurrence relation qn

my attempt:
For cos2x: use the identity cos^2(x)-sin^2(x) = (cos(x)-sin(x))(cos(x)+sin(x))

simplify the numerator and denominator, we get

|cos(x)+sin(x) +1/(cos(x)+sin(x)|

which is in the form of |a+1/a|, and the results is obvious thereafter

danielync is offline   Add to danielync's Reputation Reply With Quote
Reply

Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Q&A: About the relation of Christianity and the NewWorldOrder kujity Singapore Christian Forums 0 21st April 2012 10:39 AM
H2 mathematics Recurrence relation kickme Math Help 5 4th January 2012 04:19 PM
Public Relation Management mr forrestor Workplace and Business Forum 0 6th June 2011 11:50 AM
How to improve relation between friends symx Love & Relationships 18 1st October 2009 02:08 PM
3 yrs relatiOn sO eaSy tO brEak?? Rainee Love & Relationships 31 16th April 2007 07:07 AM

» Sponsors
Watch Free Movies Online
Celebrity Gossip
Food Delivery

» Facebook Fans
» What's Going On?
Title, Username, & Date
Repost comment.
Stupid court of appeal gives red light running driver who hit pedestrian 15% discount
Mum's Kitchen Catering and Cherish Delights get licences suspended after nearly 40 people...
[PMD-pedestrian rules] Singapore Court judges are high handed and biased or court rep
Post anything random on this thread.
Ritter Sport chocolate recalled due to undeclared allergen
Aoki Hagane no Arpeggio: Ars Nova
I really hate my mother!!!
Transcend RDF9K2 All-in-One Card Reader
Transcend ESD250C, a portable SSD that’s super classy
How PAP exploited racial differences to impose FASCIST rule over Singapore.
Up to S$7250 of government $ misused for buying each vote in Singapore?
Funky Fields organic vegan spreadable recalled due to 'undisclosed allergen'
100 hawksbill turtles released into the sea after rare hatching on Sentosa
Inspirational Songs
MOH, SFA investigating after 18 typhoid fever cases in 3 weeks
By militarily invading Hong Kong, Xi Jingping is setting in motion, the wheels of nuc
Deng XiaoPing original vision for HKG- China reunification was for the two to unite a
HSA warns against three products
Warning : Blacklist buyer/adopter Alert
Featured Photos
by marisoljames322
· · ·
Member Galleries
20359 photos
13619 comments
by marisoljames322
· · ·
Member Galleries
20359 photos
13619 comments
by pdsubbu
· · ·
Member Galleries
20359 photos
13619 comments
by Vikas Dhar
· · ·
Photography
35 photos
36 comments
by aaudreygan
· · ·
Guy Photos
1581 photos
946 comments
by aaudreygan
· · ·
Girl Photos
4351 photos
28606 comments
by a8paris
· · ·
Guy Photos
1581 photos
946 comments
by a8paris
· · ·
Guy Photos
1581 photos
946 comments
by aaricia
· · ·
Girl Photos
4351 photos
28606 comments
by aaricia
· · ·
Girl Photos
4351 photos
28606 comments

 

All times are GMT +8. The time now is 04:40 AM.


Powered by vBulletin
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
Copyright© 2004-2013 SGClub.com. All rights reserved.