1. S ECT. 9-5B M ORE T AYLOR S ERIES

2. Elementary Series

3. Manipulation Techniques We can manipulate the elementary series (or any series we are given) to find other series by using these manipulation techniques. These include: 1) Substituting into the series 2) Multiplying or dividing the series by a constant and/or a variable 3) Adding or subtracting two series 4) Differentiating or integrating a series

4. 8) Find the Maclaurin Series for Write the first four nonzero terms and the general term then use your answer for find

5. 9) Find a Power Series for centered at Write the first four nonzero terms and the general term. For what values of x does the series converge to ?

6. 10) Find the sum of Match to Elementary Series

7. 11) Find the sum of Match to Elementary Series

8. 12) Find the sum of Match to Elementary Series

9. 13) For the function a)Write the Maclaurin series for f. Give the first four nonzero terms and the general term. a)For what values of x does the series converge?

10. 14) If use the answer from 13 to a)Write the Maclaurin series for Give the first four nonzero terms and the general term. b) For what values of x does the series converge?

11. 15) Use the answer from 14 to find the sum of the infinite series

12. H OME W ORK Worksheet 9-5-B