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Linear approximations

  1. Oct 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Verify the linear approximation tanx = x at a=0.
    Then determine the values of x for which the linear approximation is accurate to within 0.1.

    2. Relevant equations
    L(x)=f(a) + f'(a) (x-a)

    3. The attempt at a solution
    Besides writing down that tanx - 0.1 < x < tanx + 0.1
    I have no idea how to approach this!
  2. jcsd
  3. Oct 2, 2007 #2


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    If you want an 'exact' answer (to some number of signficant digits) to that inequality you would have to solve it numerically. I suspect they want you to estimate a remainder term to the Taylor series. What forms of that do you know?
  4. Oct 2, 2007 #3
    I don't know what the Taylor series is. I don't think they're looking for a numerical answer though. I think they're looking for some sort of proof? I just started learning linear approximations.
  5. Oct 2, 2007 #4


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    If you don't know what a Taylor series is, forget that suggestion. Just goof around with your calculator to figure out how big x can be and still keep |x-tan(x)|<0.1. There's not really a nice way to do it.
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