Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    Edexcel P2 Jan 02
    q.7


    A curve is shown with equation f(x)=0.5ex - x2
    Curve cuts y-axis at A and the is a minimum at point B

    eqn of tangent to C at A is
    y=0.5x+0.5

    part (b)
    the x-co-ord of B is approx 2.15. A more exact estimate is found using
    xn+1=lng(xn)

    show that a possible form for g(x) is g(x)=4x

    how would I show this?
    Offline

    14
    ReputationRep:
    f(x) = 0.5e^x - x^2
    f'(x) = 0.5e^x - 2x
    at B, f'(x) = 0

    0.5e^x - 2x = 0
    e^x = 4x
    ln (e^x) = ln (4x)
    x = ln (4x)

    COnvert to an interative formula, x_(n+1) = ln (4x_n)
    so g(x) = 4x
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by mik1w)
    f(x) = 0.5e^x - x^2
    f'(x) = 0.5e^x - 2x
    at B, f'(x) = 0

    0.5e^x - 2x = 0
    e^x = 4x
    ln (e^x) = ln (4x)
    x = ln (4x)

    COnvert to an interative formula, x_(n+1) = ln (4x_n)
    so g(x) = 4x

    I follow up to x=ln(4x) wouldnt lne^x be 1^x therefore 1 not x?

    and WHAT is a interative formula?
    Offline

    0
    ReputationRep:
    (Original post by marisad_uk)
    I follow up to x=ln(4x) wouldnt lne^x be 1^x therefore 1 not x?

    and WHAT is a interative formula?
    No. lne = 1 as its log in base e of e so its 1. Therefore it just leaves x as x multiplied by 1 is just x.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by !Laxy!)
    No. lne = 1 as its log in base e of e so its 1. Therefore it just leaves x as x multiplied by 1 is just x.
    sorry for sounding stupid but i am still confused

    lne=logee=1

    lnex =1x
    1x =1 :confused:
    • Thread Starter
    Offline

    2
    ReputationRep:
    sorry but i gotta *bump*
 
 
 
Turn on thread page Beta
Updated: June 19, 2005
The home of Results and Clearing

3,403

people online now

1,567,000

students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Poll
Will you be tempted to trade up and get out of your firm offer on results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.