Taylor Polynomial Error

Discussion in 'Math' started by meichberg92, May 12, 2014.

  1. meichberg92

    Thread Starter New Member

    May 12, 2014
    2
    0
    Hey I need help with this problem guys!


    How do I find, using Taylor's Theorem, the error of the taylor polynomial of f(x)=sqrt(x) of degree 2 to approximate sqrt(8)?

    and, find a bound on the difference of sin(x) and x- x^3/6 + x^5/120 for x in [0,1]
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,179
    1,800
  3. meichberg92

    Thread Starter New Member

    May 12, 2014
    2
    0
    What about the second question? I dont think that has to do with it.
     
  4. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
  5. Papabravo

    Expert

    Feb 24, 2006
    10,179
    1,800
    I think that sin(x) and the polynomial you gave are equivalent for the first three terms. Since this is an alternating series, a bound should be the absolute value of the next term.
     
    Last edited: May 13, 2014
  6. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    Well spotted papabravo!

    Of course there are only three terms stated in the second part.
     
  7. Papabravo

    Expert

    Feb 24, 2006
    10,179
    1,800
    There might possibly be better bounds. For example a Chebyshev approximation has a much better absolute error bound for a given number of terms over the entire interval of approximation, which is typically [-1,1]
     
Loading...