Taylor Polynomials with Remainder
In all the following exercises,
is taken as
Let
The 5th Tayor polynomila for
is
and
Using
these formulas, or otherwise, find find
and for
for the functions
Use
for the function
to approximate
and
Determine the accuracy of this approximation knowing that
.
Determine
for
and for
For
find
and
Use your results to approximate
and give the error exacly and using the formula for
Find
for
and use your results to approximate
and
Which result is a better approximation of the corresponding true value?
Suggest a way to obtain better accuracy for the less accurate result.
Find
for
and then use your results to estimate the accuracy acheived when using
to approximate
on the interval
In the previous exercise, aproximate
and
by replacing
by
For the function
find
and
Find the Taylor polynomial of least degree to approximate
to
accuracy on the interval
and use it to approximate
On an Excel sheet draw the graphs of the functions
and its Taylor polynomials
over the interval