Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    (1+x)^-1
    (1-3x)^½
    a)use on of these expansions with a suitable value of x, to estimate the value of 1/1.001 correct to 6sf

    b) use both your answers from the above binomail expansions find the first 4 terms in the series expansion of √(1-3x)/(1+x), stating the set if values of x for which the expansion is valid
    Offline

    20
    ReputationRep:
    (Original post by lil_kk)
    (1+x)^-1
    (1-3x)^½
    a)use on of these expansions with a suitable value of x, to estimate the value of 1/1.001 correct to 6sf
    let x = 0.001 in the expansion (1+x)-1 as far as x² this should give you 5 d.p or 6 sig fig accuracy...

    1 + -1(x) + -1*-2(x)²/2! + ....
    Offline

    20
    ReputationRep:
    (Original post by lil_kk)
    find the first 4 terms in the series expansion of √(1-3x)/(1+x), stating the set if values of x for which the expansion is valid
    {1 + ½(-3x) + ½*-½(-3x)²/2! + ½*-½*-1.5(-3x)³/3!+ ...}{ 1 + -1(x) + -1*-2(x)²/2! + -1*-2*-3(x)³/3! + ...}

    now simplify inside the brackets. when you have simplified you multiply out the brackets, discarding any terms involving powers of x greater than 3.

    the first expansion is valid for -1<3x<1 or -1/3 < x < 1/3
    the second expansion is valid for -1< x < 1

    the combined expansion is valid for the more restrictive of the two ranges ie
    -1/3 < x < 1/3
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by the bear)
    {1 + ½(-3x) + ½*-½(-3x)²/2! + ½*-½*-1.5(-3x)³/3!+ ...}{ 1 + -1(x) + -1*-2(x)²/2! + -1*-2*-3(x)³/3! + ...}

    now simplify inside the brackets. when you have simplified you multiply out the brackets, discarding any terms involving powers of x greater than 3.

    the first expansion is valid for -1<3x<1 or -1/3 < x < 1/3
    the second expansion is valid for -1< x < 1

    the combined expansion is valid for the more restrictive of the two ranges ie
    -1/3 < x < 1/3
    thanks for your help
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 24, 2005

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.