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Taylor Polynomials and Numerical Analysis

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6.

    *To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use.

    2. Relevant equations
    x = 45 or pi/4, x0 = 42 or 7pi/30

    cos(x) = Pn(x) + Rn(x)

    Polynomial Term - Pn(x) = ∑f^(k)(x-x0)^k/(k)!

    Error Term - Rn(x) = f^(n+1)(ζ(x))(x-x0)^(n+1)/(n+1)!

    3. The attempt at a solution
    (pi/60)^n/(n+1)! < ((-60/pi)*10^-6)/pi

    ^I get stuck at this part. I'm supposed to solve for n, but the left-hand side of this inequality confuses me.
     
  2. jcsd
  3. Jan 27, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    What are you doing? We have ##|\text{error}| \leq (\pi/60)^{n+1}/(n+1)!##, and this must not exceed ##10^{-6}##.
     
  4. Jan 28, 2014 #3

    joshmccraney

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    Gold Member

    this is pretty tough to read. perhaps put it in latex and then we can check it out
     
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