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Calculus 2 Lesson 11.11 Applications of Taylor Series |
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| The following topics
are the most important. Typical exercises from Calculus, 7th edition-Early
Transcendentals, by James Stewart, are
assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective. |
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| 1. | Find the Taylor or
Maclaurin polynomial Tn(x) for a function f at a number a. Show how well the Tn's approximate f by doing the following. |
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| 1a. | Graph f and several Tn's on the same set of axes. P774#1,3,5 | |
| P768 | The definition of Taylor polynomial Tn is given in the middle of the page. | |
| P769 | The definition of Taylor remainder Rn is given on this page. | |
| P769 | The example in the left hand margin on this page gives the process. | |
| 1b. | Evaluate f and several Tn's at the same x value. P775#23 | |
| P769 | Example 1 shows this method on this page. | |
| P769 | Watch the video in the ebook in webassign. Example 1 | |
| 2. | For a given function f, | |
| 2a. | Approximate values of the function using the Taylor or Maclaurin polynomial. | |
| P770 | Example 2 part a shows this approach. | |
| P770 | Watch the video in the ebook in webassign. Example 2 | |
| 2b. | Find an upper bound for the error above by bounding the remainder term using Taylor's inequality. P774#13,15 | |
| P771 | Example 2 part b shows this approach. | |
| Maple Assignment: none | ||