Since I went a little fast at the end, I am sending you the last two 
Matlab programs that I've written on the board:


   function s = myExp(x, tol)
   s = 1;  n = 1;  an = 1;
   while  ( abs(an) > tol) 
       an = x^n / factorial(n);
       s = s + an;
       n = n + 1;
   end;


   function s = myExp2(x, tol)
   s = 1;  n = 1;  an = 1;
   while  ( abs(an) > tol) 
       an = an * x / n;
       s = s + an;
       n = n + 1;
   end;


Note that in the first program I am starting summation with term n=1, 
and add the term n=0 at the initialization (s=an=1) ; this way the two 
functions look more similar. The second program makes use of the 
recursion relationship between terms: a(n-1) = a(n) * x / n.

Note that the two programs are formally completely equivalent; make 
sure you understand what each command does. However, myExp(x,tol) only 
works for values of x up to about 50, while the function myExp2(x,tol)  
runs for x as large as 600. Please practice by running the two programs 
for different values of x, and compare the result with the true value 
exp(x).