Convergence of Taylor Series for Various Functions

[Berdi]

Homework Statement

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

Homework Equations

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?

 

[zcd]

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