A command useful for generating sequences of numbers, functions
etc. arising from one `formula' is seq. Observe the result of executing
the following statements
seq( i^2, i=3..7 );
seq( i^2, i={3,4,10,20} );
seq( sin(k*x), k=0..4 );
We now apply this to compare the graphs of 
and the Taylor
expansions of 
(around x=0) of orders 1,3,5,7, over the
interval 
.
readlib(mtaylor):
tay := proc(i) if type(i,numeric) Line Feed
then mtaylor( sin(x), [x=0], i+1 ) Line Feed
else 'tay'(i) fi Line Feed
end:
polylist := seq( tay(i), i={1,3,5,7} ); list of polynomial approx.
plot( {sin(x), polylist}, x=-2*Pi..2*Pi, y=-2..2 );
Pick out the graph of 
- it is the periodic one - and judge the
quality of the approximations by the Taylor polynomials.