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Homework Help: Really need help - Taylor Polynomial Approximation Error

  1. Apr 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Use Taylor's theorem to obtain an upper bound of the error of the approximation. Then calculate the exact value of the error.

    cos(.3) is approximately equal to 1 - (.3)^2/2! + (.3)^4/4!

    2. Relevant equations

    3. The attempt at a solution

    I came up with upper bound saying

    Rn = (-sinz/5!)*(.3)^5 < (.3)^5/5!

    so the upper bound is (.3)^5/5! which is about .00002

    But for the exact error I have no idea how to calculate it. There aren't any examples in my textbook.
  2. jcsd
  3. Apr 10, 2008 #2


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    I think they want you to use a calculator to actually find cos(.3) then subtract the approximation to see if how well your estimate worked.
  4. Apr 10, 2008 #3


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    Homework Helper

    The only way to calculate the exact value of the error is to take the exact value of the cosine and subtract the value of the series. I think they just mean punch cos(.3) into your calculator and then subtract the series value and see that it's less than the remainder term.
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