Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    For this question, why do you not use Taylor's expansion with a=8? Is it only when a function is translated horizontally where you don't use a=0?

    Also, why do you use x instead of e^x in the expansion? Would using e^x give you the same answer?

    Thanks for any help!
    Attached Images
      
    Offline

    22
    ReputationRep:
    (Original post by PhyM23)
    For this question, why do you not use Taylor's expansion with a=8? Is it only when a function is translated horizontally where you don't use a=0?

    Also, why do you use x instead of e^x in the expansion? Would using e^x give you the same answer?

    Thanks for any help!
    The question wants the expansion in powers of x and not powers of (x-a), which is where you'd use the Taylor expansion.

    I don't understand your second question.
    Offline

    14
    ReputationRep:
    The series expansion of a function is taken from 0,0 if nothing else is stated as a baseline. Also it wants in powers of x

    Maclaurin series states that:
    f(x)=f(0)+f'(0)x+\frac{f''(0)}{2  !}x^{2}+\frac{f'''(0)}{3!}x^{3}+  \cdots

    Hence x is used in the expansion. However, e^{x} would not give the same answer.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    The question wants the expansion in powers of x and not powers of (x-a), which is where you'd use the Taylor expansion.

    I don't understand your second question.
    Thanks for the reply

    But why couldn't you use f(x) = f(a) + xf ' (a) ... with a=8?

    I mean why do you use x(f'(0)) + ((x^2)/2)f''(0)? Why aren't the 'x's in this expansion 'e^x's?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Cryptokyo)
    The series expansion of a function is taken from 0,0 if nothing else is stated as a baseline. Also it wants in powers of x

    Maclaurin series states that:
    f(x)=f(0)+f'(0)x+\frac{f''(0)}{2  !}x^{2}+\frac{f'''(0)}{3!}x^{3}+  \cdots

    Hence x is used in the expansion. However, e^{x} would not give the same answer.
    Thanks for the reply!

    But in my textbook it says 'Express tan(x+pi/4)as a series in ascending powers of x up to the term x^3' and they've used a=pi/4. Why don't they use a=0?
    Offline

    22
    ReputationRep:
    (Original post by PhyM23)
    Thanks for the reply

    But why couldn't you use f(x) = f(a) + xf ' (a) ... with a=8?

    I mean why do you use x(f'(0)) + ((x^2)/2)f''(0)? Why aren't the 'x's in this expansion 'e^x's?
    What you've written down is incorrect.

    f(x) = f(a) + xf ' a() + ...

    The correct version is:

    f(x) = f(a) + (x-a)f ' (a) + ...

    Or:

    f(x+a) = f(a) + x f' (a) + ....

    But f(x+a) is not y, so is useless here.

    Second of all, the question wants an expansion in powers of x, not e^x.
    Offline

    14
    ReputationRep:
    (Original post by PhyM23)
    Thanks for the reply!

    But in my textbook it says 'Express tan(x+pi/4)as a series in ascending powers of x up to the term x^3' and they've used a=pi/4. Why don't they use a=0?
    You could use a=8 but it wants each power of x in its simplest form and
    f(x)=f(8)+f'(8)(x-8)+\frac{f''(8)}{2!}(x-8)^{2}+\cdots
    is not each term in its simplest form. If you expanded the brackets and then made each power of x into its simplest form it would give the correct answer. But this is much more involved.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    What you've written down is incorrect.

    f(x) = f(a) + xf ' a() + ...

    The correct version is:

    f(x) = f(a) + (x-a)f ' (a) + ...

    Or:

    f(x+a) = f(a) + x f' (a) + ....

    But f(x+a) is not y, so is useless here.

    Second of all, the question wants an expansion in powers of x, not e^x.

    Ah my apologies I did mean f(x+a). What you've said makes sense. Thanks for clearing this up.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Cryptokyo)
    You could use a=8 but it wants each power of x in its simplest form and
    f(x)=f(8)+f'(8)(x-8)+\frac{f''(8)}{2!}(x-8)^{2}+\cdots
    is not each term in its simplest form. If you expanded the brackets and then made each power of x into its simplest form it would give the correct answer. But this is much more involved.
    Thank you for this; it's very helpful!
    Offline

    22
    ReputationRep:
    No problem!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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