Mathematical Principles for Scientific Computing and Visualization  
http://www.farinhansford.com/books/scv
by Gerald Farin and Dianne Hansford


This notebook demonstrates the Taylor series approximation to the Exp function.
Two things to play with: 
1) The number of polynomial terms in the series approximation -- see 'approxnum'
2) The range over which we plot Exp and its approximation, called series here.
As the range increases, the number of terms needed increases.


See Chapter 2: Computational Basics for details.

approxnum = 20;
series[x_]:=Sum[(x^i)/Factorial[i],{i,0,approxnum}];

min = -5;
max = 8;

Plot[series[x],{x,min,max}]
Plot[Exp[x],{x,min,max}]