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Taylor Polynomial approximation

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data
    obtain the number r = √15 -3 as an approximation to the nonzero root of the equation x^2 = sinx by using the cubic Taylor polynomial approximation to sinx


    2. Relevant equations
    cubic taylor polynomial of sinx = x- x^3/3!


    3. The attempt at a solution
    Sinx = x-x^3/3! + E(x)
    x^2 = x-x^3/6+ E(x)


    How do I able to obtain the r?
     
    Last edited: Feb 6, 2013
  2. jcsd
  3. Feb 6, 2013 #2

    jbunniii

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    In order to get exact equality you need
    $$\sin(x) = x - x^3/6 + E(x)$$
    where ##E(x)## is the error due to using only two terms. As an approximation, we assume this error to be zero, so we pretend that
    $$\sin(x) = x - x^3/6$$
    and solve the equation
    $$x^2 = x - x^3/6$$
     
  4. Feb 6, 2013 #3
    But how do I able to obtain the number r?
     
  5. Feb 6, 2013 #4

    jbunniii

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    As the problem statement says, ##r## is a nonzero root of the equation ##x^2 = \sin(x)##. You will find an approximation to this by solving the equation ##x^2 = x - x^3/6##.
     
  6. Feb 6, 2013 #5
    Solved, thanks!
     
    Last edited: Feb 6, 2013
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