Taylor development

1. Mar 14, 2017

PeteSampras

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

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

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

$$(\frac{x^4}{x^5+1})^{-1/2}$$

but, for example wolfram yield a solution f approx x2

http://www.wolframalpha.com/widget/...0&podSelect=&showAssumptions=1&showWarnings=1

2. Mar 14, 2017

Staff: Mentor

Isn't it when $x_0 = 1$ that is the problem where it's not differentiable?

3. Mar 14, 2017

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).

4. Mar 14, 2017

John Park

If you complete the calculation of f' by the chain rule, I think you'l find that factor isn't a problem.