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Thread: Approximate Expression from Taylor Expansion: f(x)=(a/x)^(12)-2(a/x)^6

  1. #1

    Approximate Expression from Taylor Expansion: f(x)=(a/x)^(12)-2(a/x)^6

    Given:
    f(x)=(a/x)12-2(a/x)6
    Use a Taylor Expansion about x=a to obtain an approximate expression for f(h), where h=x-a, to a second order in h.

    So I've found:
    f'(x)=12a6/x7-12a12/x13
    f''(x)=156a12/x14-84a6/x8

    And evaluated at x=a:
    f(a)=-1
    f'(a)=0
    f''(a)=72/a2

    This gives the expansion:
    f(x)=36(x-a)2/a2-1

    I thougt at this point, I could then do f(h) or f(x-a) by substituting x=h or x=x-a, but the answer is expected to be only in terms of h, so I am not sure what to do next.
    Any help would be much appreciated

  2. #2
    Elite Member
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    Jan 2012
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    If the answer is "expected to be only in terms of h" then use h= x-a which is what the problem told you: [tex]\frac{36}{a^2}h^2- 1[/tex].

  3. #3
    Which is what I thought, but I can't have an a term apparently.

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