P a g e
While it is truly elegant that Taylor series exactly converge to functions (on their interval of convergence), it is
the inexact Taylor polynomials that essentially do all of the work.
Let’s ponder this for a minute…
can be found
by summing an infinite Taylor series, if we
want to use that information to find
, we will have to evaluate Taylor polynomials until we arrive at an
with which we are satisfied.
Approximating a Function to Specifications
Find a Taylor polynomial that will serve as a substitute for
on the interval
such that the error
between the Taylor polynomial approximation and
is less than 0.0001 for all