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Remainder Estimation Theorem

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the maximum error in approximating cos(x) by its Taylor polynomial of order 2 on the
    interval [
    −.25, .25]. Justify your answer using the Remainder Estimation Theorem.



    2. Relevant equations
    |R3(x)<=M/3! |x|^3


    3. The attempt at a solution
    |R3(x)<=M/3! |x|^3 Plugging in the 3 is easy enough, but I don't understand where the M comes from. What is M here? I initally thought it might be the value of the 4th taylor polynomial, but that would make the remainder less than or = zero, right?
     
  2. jcsd
  3. Mar 25, 2009 #2
    M is the maximum of the absolute value of the 3rd derivative of cos(x) on [-1/4,1/4].
     
  4. Mar 25, 2009 #3
    Thank you so much!
     
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