MATH 151: Calculus II

Test #2 Review Topics

March 26, 2019

1. Computing volumes with the cylindrical shells method

2. Parametric equations of curves; conversions from non-parametric to parametric and vice versa

3. Arc length in parametric and non-parametric forms

4. Polar coordinates: graphing curves, intersections, arc lengths

5. Average value of a function in an interval

6. Applications of integration to mechanics: computing work done when stretching springs or moving objects

7. Probability density function

8. Uniform, exponential, and normal density functions

9. Mean (expected value) of a probability density function

10. Sequences: explicit and recursive definitions

11. Limit of a sequence: definition, meaning, convergence vs. divergence

12. Theorems about limits of sequences: function, squeeze, absolute value, continuous function

13. Monotonic and bounded sequences

14. Geometric sequence and its limit

15. Series: definition and convergence; partial sums; summation notation

16. Geometric series, finite and infinite

17. Repeating decimals as rational numbers

18. Telescoping series

19. Theorem about convergent series and its consequences

Optional review problems:

Chapter 6 Review: 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 35, 37, 38, 39.

Chapter 8 Review: 1, 3, 5, 7, 14, 23.

Appendix H1: 8, 9, 11

Appendix H2: 31

Additional office hours on Thursday: 2 - 4