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Homework Help: Taylor Series - Convergence

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data

    For what values of x (or [tex]\theta[/tex] or u as appropriate) do you expect the following Taylor Series to converge? DO NOT work out the series.

    [tex]\sqrt{x^{2}-x-2}[/tex] about x = 1/3

    [tex]sin(1-\theta^{2}) [/tex] about [tex]\theta = 0[/tex]

    [tex]tanh (u) [/tex] about u =1

    2. Relevant equations

    3. The attempt at a solution

    I'm not to sure where to begin. Taylor series have a radius of convergence where |x-a|< R, wher a is the nearest singularity, so I suppose that's a starting point?
  2. jcsd
  3. Nov 22, 2009 #2


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    For what domain is [tex]\sqrt{x^{2}-x-2}[/tex] defined? It can't converge beyond that.
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