# Taylor Series - Convergence

1. Nov 22, 2009

### Berdi

1. The problem statement, all variables and given/known data

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

$$\sqrt{x^{2}-x-2}$$ about x = 1/3

$$sin(1-\theta^{2})$$ about $$\theta = 0$$

$$tanh (u)$$ 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. Nov 22, 2009

### zcd

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