Plot several degrees of Taylor polynomial of
For each, give the interval on which the polynomial is close to the
function f(x). You should decide how close is ``close to f(x).'' One
way to measure the interval is to plot the absolute value of the difference
between the function and the Taylor polynomial.
What happens to the interval as the degree
of the polynomial gets larger? Why is it reasonable to expect that two
Taylor polynomials of high degree will agree on a fairly large interval?