Question

Do we have a mathematical explanation of our taylor approximation gets worse the farther we get from point a which is the basis for taylor approximation?

Answer 1

http://en.wikipedia.org/w/index.php?title=File:Sintay.svg&page=1

Answer 2

Yea i see that but do we have a mathematical arguement that is not a graph? fx. the function i work with atm. is ln(x) and useing the 49'th taylor approximation a=1
and get the following values:
ln(2.1)=0.749137
T49(ln(2,1))=1.871667