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Taylor development

  1. Mar 14, 2017 #1
    1. The problem statement, all variables and given/known data
    Is it possible obtain a Taylor serie at x0=0?

    2. Relevant equations
    [tex]f(x)= (\frac{x^4}{x^5+1})^{1/2} [/tex]

    3. The attempt at a solution
    I think that it is not possible , since f' is not differenciable at x=0, since f' have the factor

    [tex](\frac{x^4}{x^5+1})^{-1/2} [/tex]

    but, for example wolfram yield a solution f approx x2

  2. jcsd
  3. Mar 14, 2017 #2


    Staff: Mentor

    Isn't it when ##x_0 = 1## that is the problem where it's not differentiable?
  4. Mar 14, 2017 #3


    Staff: Mentor

    f is continuous at 0, f' is continuous at 0, f'' is continuous at 0...
    The function you're working with definitely has a Maclaurin series (i.e., a Taylor series in powers of x).
  5. Mar 14, 2017 #4
    If you complete the calculation of f' by the chain rule, I think you'l find that factor isn't a problem.
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