Calculus lets you approximate complicated functions with power series.
Mathematica lets you generate and work with power series for a huge range of functions.
Use
Series to make a power series out of a function. The first argument is the function. The second argument has the form
{var, pt, order}, where
var is the variable,
pt is the point around which to expand, and
order is the order:
The "big-O" notation
O[x]6 indicates that terms beyond
x5 are omitted:
Truncate the series to get a polynomial of degree 5 using
Normal:
At
, compare the polynomial and the original exponential function:
