MATH 151: Calculus II

Test #3 Review Topics

April 19, 2019

1. The integral test of convergence

2. p-series and its convergence

3. The comparison test of convergence

4. The limit comparison test of convergence

5. Remainder estimate for the integral test *)

6. Estimating the sum of a series with the use of remainder estimate for integral test

7. The alternating series test

8. Alternating series estimation theorem *)

9. Absolute convergence

10. The ratio test

11. Power series: definition, three cases of convergence, radius of convergence

12. Differentiation and integration of power series, preservation of radius of convergence

13. Taylor and Maclaurin series; derivation of Taylor series coefficients

14. Important Maclaurin series and their radii of convergence *)

15. Taylor polynomial and Taylor remainder

NOTE: The formulas for items marked with asterisks will be provided.

Optional review problems:

Chapter 8 Review: 9, 11, 12, 13, 14, 15, 17, 19, 22, 26, 27, 29, 33, 35, 37, 39, 41, 43

Additional office hours:
Thursday, April 25: 2:30 - 5:00