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Remainder Estimation Theorem

  • Thread starter negatifzeo
  • Start date
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?
M is the maximum of the absolute value of the 3rd derivative of cos(x) on [-1/4,1/4].
Thank you so much!

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