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Homework Help: Taylor Expansion and Error

  1. Apr 2, 2007 #1
    1. The problem statement, all variables and given/known data
    For g=Hf = sin (f), use a Taylor expansion to determine the range of input for which the operator is approximately linear within 10 %


    2. Relevant equations
    The taylor series from 0 to 1 , the linearization, is the most appropriate equation

    3. The attempt at a solution

    g(f) = sin(0) + f*cos(0) = f
    g1(f) = sin(f) g2 (f) =f ( at f=0, g1=g2(f) )

    g1(f) = g2(f) + error

    sin(f) = f + (1/10) * sin (f)

    (9/10)* sin (f) =f

    the value I keep getting is when f is equal to 0. I really don't think I am doing this correctly. Any advice?
     
  2. jcsd
  3. Apr 3, 2007 #2

    HallsofIvy

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    Science Advisor

    The only place sin(f)- f= (1/10)sin(f) is at f= 0 but if one is positive and the other negative you can still compare them. Your "error" is |sin(f)- f| and you want that less than |(1/10)sin(f)|. Where are those equal?
     
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