1. Monday, Oct 26, 2015MAT 146 Test #3! NO CALCULATOR! Thursday (STV 229) CALCULATOR OK! Friday (STV 219)

2. Monday, Oct 26, 2015MAT 146

3. Monday, Oct 26, 2015MAT 146

4. Monday, Oct 26, 2015MAT 146 Sequence Characteristics Convergence/Divergence: As we look at more and more terms in the sequence, do those terms have a limit? Increasing/Decreasing: Are the terms of the sequence growing larger, growing smaller, or neither? A sequence that is strictly increasing or strictly decreasing is called a monotonic sequence. Boundedness: Are there values we can stipulate that describe the upper or lower limits of the sequence?

5. Monday, Oct 26, 2015MAT 146

6. Monday, Oct 26, 2015MAT 146 On of our goals this chapter is to generate polynomial functions that can be used to approximate other functions near particular values of x. The polynomial we seek is of the following form:

7. Monday, Oct 26, 2015MAT 146

8. Monday, Oct 26, 2015MAT 146

9. Monday, Oct 26, 2015MAT 146

10. Monday, Oct 26, 2015MAT 146 Goal: Generate polynomial functions to approximate other functions near particular values of x. Create a third-degree polynomial approximator for

11. Monday, Oct 26, 2015MAT 146 Create a 3rd-degree polynomial approximator for

12. Monday, Oct 26, 2015MAT 146 We start with a sequence {a n }, n going from 1 to ∞, and define {s i } as shown. The {s i } are called partial sums. These partial sums themselves form a sequence. An infinite series is the summation of an infinite number of terms of the sequence {a n }.

13. Monday, Oct 26, 2015MAT 146 Our goal is to determine whether an infinite series converges or diverges. It must do one or the other. If the sequence of partial sums {s i } has a finite limit as n −−> ∞, we say that the infinite series converges. Otherwise, it diverges.

14. Monday, Oct 26, 2015MAT 146 A geometric series is created from a sequence whose successive terms have a common ratio. When will a geometric series converge?

15. Monday, Oct 26, 2015MAT 146 The harmonic series is the sum of all possible unit fractions.

16. Monday, Oct 26, 2015MAT 146 A telescoping sum can be compressed into just a few terms.

17. Monday, Oct 26, 2015MAT 146

18. Monday, Oct 26, 2015MAT 146 Spreading a Rumor: Suppose that y represents the number of people that know a rumor at time t and that there are M people in the population. For these parameters, one model for the spread of the rumor is that “the rate at which the rumor is spread is proportional to the product of those who have heard the rumor and those who have not heard it.”

19. Monday, Oct 26, 2015MAT 146 Details... details... details! https://plus.maths.org/content/teacher- package-differential-equations