Remainder Estimation Theorem

  • Thread starter negatifzeo
  • Start date
  • #1
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Homework Statement


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.



Homework Equations


|R3(x)<=M/3! |x|^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?
 

Answers and Replies

  • #2
M is the maximum of the absolute value of the 3rd derivative of cos(x) on [-1/4,1/4].
 
  • #3
66
0
Thank you so much!
 

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