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Taylor Polynomial Approximation

  1. Jan 7, 2008 #1
    How to find a polynomial P(x) of the smallest degree such that sin(x-x^2)=P(x)+o(x) as x->0?
    Do I have to calculate the first six derivatives of f(x)=sin(x-x^2) to get Taylor polynomial approximation?
     
  2. jcsd
  3. Jan 7, 2008 #2

    HallsofIvy

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    If you know the Taylor series expansion for sin(x) you don't need to calculate any derivatives at all. Just replace x in the expansion with x- x2.

    [itex]sin(x)= x- x^3/6+ x^5/5!+ \cdot\cdot\cdot [/itex].
    [itex]sin(x-x^2)= (x-x^2)- (x-x^2)^3+ (x-x^2)^5/5!+ \cdot\cdot\cdot[/itex]
     
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