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F(x)=sinx with taylor's theorem

  1. Dec 6, 2008 #1
    i. Expand f(x)= x^5+x^3+x in powers of (x-1), using Taylor's theorem
    ii. Consider f(x)= sin x. Find the Taylor polynomial T of degree 7 expanded at [tex]\pi\[/tex]/3.
    Give an estimate for the remainder term, in the form
    |sin (x)- T(x)|[tex]\leq[/tex] C|x-[tex]\pi[/tex]/3|^8
    with a suitable (good) constant C.

    f(x)= f(1)+f'(1)(x-1)+f''(1)(x-1)^2.... + f^(n)(1)/n!(x-1)^(n)
    is that right for i?
    and for ii... i'm not sure what to do.
  2. jcsd
  3. Dec 6, 2008 #2


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    For i, it is technically correct, but you are given the function. So work out the derivatives!

    For ii, start by writing down the Taylor series, for n running up to 7.
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