Taylor Polynomials with Remainder

In all the following exercises, is taken as

1. Let The 5th Tayor polynomila for is

and

Using these formulas, or otherwise, find find and for for the functions

2. Use for the function to approximate and Determine the accuracy of this approximation knowing that .

3. Determine for and for

4. For find and Use your results to approximate and give the error exacly and using the formula for

5. 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.

6. Find for and then use your results to estimate the accuracy acheived when using to approximate on the interval

7. In the previous exercise, aproximate and by replacing by

8. For the function find and Find the Taylor polynomial of least degree to approximate to accuracy on the interval and use it to approximate

9. On an Excel sheet draw the graphs of the functions and its Taylor polynomials over the interval

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