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Please help me (taylor series)

  1. Apr 21, 2006 #1
    can someone please let me know whether this is right or wrong please?


    here are the directions:

    Please find the taylor series for f(x) cntered at the given value of a.

    and the question:

    f(x)= lnx a= 2

    i dont get how to do this since the maclaurin series for ln(x) isnt given....

    EDIT: thanks bomba for explaining. can someone just please let me know if this is right or wrong? thanks:
    Last edited: Apr 21, 2006
  2. jcsd
  3. Apr 21, 2006 #2
    :wink: Hint:
    [tex]f\left( x \right) = \sum\limits_{n = 0}^\infty {\frac{{f^{\left( n \right)} \left( a \right)}}{{n!}}\left( {x - a} \right)^n }[/tex]
  4. Apr 21, 2006 #3

    can someone please check it for me? it doesnt look right
  5. Apr 21, 2006 #4


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    Staff Emeritus
    Science Advisor

    The formula you have in your first post is clearly incorrect because of that "ln 2". As Bomba told you, the coefficient of (x-2)n is
    f(x)= ln x so f(2)= ln 2: that's the constant term
    f'(x)= 1/x f'(2)= 1/2: the coefficient of (x-2) is 1/2 (no ln 2 in it!)
    f"(x)= -1/x2 f"(2)= -1/4: the coefficient of (x-2)2 is (-1/4)/2= -1/8.

    Can you work out the general term?
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