Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    17
    ReputationRep:
    How do we work out a validity interval for a Maclaurin series? I've seen that with something such as ln(1 - 3x), the interval is -1 < -3x < 1, so -(1/3) < x < (1/3).

    My intuition says that we take the x multiple, slap it in the middle and take the constants and put them at either side, making one positive and one negative.
    But I doubt this rule follows for everything.

    So what do we generally do to find the validity interval for a Maclaurin series?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Heirio)
    How do we work out a validity interval for a Maclaurin series? I've seen that with something such as ln(1 - 3x), the interval is -1 < -3x < 1, so -(1/3) < x < (1/3).

    My intuition says that we take the x multiple, slap it in the middle and take the constants and put them at either side, making one positive and one negative.
    But I doubt this rule follows for everything.

    So what do we generally do to find the validity interval for a Maclaurin series?
    When you have something like \ln(2-5x) or something, get in the form that is in the formula booklet. That is \ln(1+x). So you want to get something like \ln(1+[\text{something that is between -1 and 1}])

    This is simple as \ln(2-5x)=\ln(2)+\ln(1-\frac{5}{2}x) which for easy comparison can be written as \ln(2)+\ln(1+(-\frac{5}{2}x))

    Now here that 'something' is clearly -\frac{5}{2}x, so say -1&lt;-\frac{5}{2}x&lt;1 and so get the answers of -\frac{2}{5}&lt;x&lt;\frac{2}{5} by some basic rearranging.
    • Thread Starter
    Offline

    17
    ReputationRep:
    I see. I saw on the powerpoint I'm using to revise that another expression that requires a validity interval is (1 + x)^n. Are there any more kinds of expressions apart from the two I've mentioned in this thread and do we work them out in the same way?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Heirio)
    I see. I saw on the powerpoint I'm using to revise that another expression that requires a validity interval is (1 + x)^n. Are there any more kinds of expressions apart from the two I've mentioned in this thread and do we work them out in the same way?
    Yes the principle carries over, and yes there are other expressions but at A-Level it's just those 2 I think.
    • Thread Starter
    Offline

    17
    ReputationRep:
    I see, so the rule you described is the only one I need for my studies atm? That's good.

    A small question though, you said we put it into a different form, so ln(2 - 5x) becomes ln2 + ln(1 - 5x/2). If we're using the right hand side of the expression, what happens to the ln2? Do we simply disregard it?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Heirio)
    I see, so the rule you described is the only one I need for my studies atm? That's good.

    A small question though, you said we put it into a different form, so ln(2 - 5x) becomes ln2 + ln(1 - 5x/2). If we're using the right hand side of the expression, what happens to the ln2? Do we simply disregard it?
    It's a constant outside the variable function. It doesn't affect the interval of validity, so we don't need to touch it as far as the validity is concerned.

    And it's not so much of a 'rule' - it's just how I remember it. You may find an easier way and stick with that one, whatever gets the job done.
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by RDKGames)
    It's a constant outside the variable function. It doesn't affect the interval of validity, so we don't need to touch it as far as the validity is concerned.

    And it's not so much of a 'rule' - it's just how I remember it. You may find an easier way and stick with that one, whatever gets the job done.
    yeah that all sounds good
    thanks for the help!
    Posted on the TSR App. Download from Apple or Google Play
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 27, 2017
Poll
Do you like carrot cake?
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.