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

1.  2.  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  This document created by Scientific WorkPlace 4.0.

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