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Calculus 2 Lesson 11.6 Absolute Convergence |
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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. | Define "absolute convergence" and "conditional convergence". Text P732&733 | ||
| P732 | The definition of absolute convergence is given in box 1 on this page. The theorem in box 3 on the next page is a result that you need to know. Look at Example 1. | ||
| P733 | The definition of conditional convergence is given in box 2 on this page. Look at Example 2. | ||
| P733 | To conclude that a series is conditionally convergent, you must use two tests: one to show that the series is not absolutely convergent and another to show that the series is convergent. | ||
| 2. | Determine whether a series is absolutely convergent, conditionally convergent or divergent using among other things, | ||
| 2a. | the previous methods, P737#5,10,17 | ||
| P733 | We use absolute convergence when the the terms do not alternate but some terms are positive and some are negative. Look at Example 3. | ||
| P733 | Look at the video in the ebook on Webassign. Example 3 | ||
| 2b. | the ratio test, P737#1,3,8,13,29 | ||
| P734 | The definition is given in the box at the top of this page. Look at Examples 4 and 5. | ||
| P736 | Look at the video in the ebook on Webassign. Example 5 | ||
| 2c. | the root test. P738#21,23 | ||
| P736 | The definition is given in the box in the middle of this page. Look at Example 6. | ||
| P736 | Look at the video in the ebook on Webassign. Example 6 | ||
| Maple Assignment: none | |||