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