Background
As background, I have found that taylor expansion provides poor estimates of a function at extreme parameter values. Indeed, the approximation at extreme values can get worse (more rapid exponential increase) as the order of the taylor series increases.
This seems intuitive, but I don't know that it is a rule... or if there is a proof.
Questions
- Do all polynomials with order $> 1$ go to $\pm$ infinity?
- Is there a good reference where I can find answers to a qustion such as this?