1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook