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Homework Help: What did I do wrong here? (expressing root x as taylor series about a=4)

  1. Mar 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Here is the question:

    nxh3n.png

    I don't quite know what I did wrong. My method is below.

    2. Relevant equations



    3. The attempt at a solution

    f(x)=√x
    f'(x)=[itex]\frac{1}{2(x)^{1/2}}[/itex]
    f''(x)=[itex]\frac{-1}{(2)(2)(x^{3/2}}[/itex]

    a=4
    f(a)=2
    f'(a)=1/4
    f''(a)=[itex]\frac{-1}{4(4^{3})^{1/2}}[/itex]

    so wouldn't the second taylor polynomial be what I put in the answer field above? Thanks.
     
  2. jcsd
  3. Mar 16, 2012 #2

    SammyS

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    What you have is the degree 2 term (almost). What's the sign?

    Include the constant term & the linear term.
     
  4. Mar 16, 2012 #3
    Oh, so if it asks for T[itex]_{2}[/itex] it also wants the T[itex]_{1}[/itex] and the constant term as well?

    Also, I see now that I somehow dropped a negative sign. Thanks!

    EDIT: I just tried it and it's correct, so I answered my own question. But thanks again!
     
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