## Class Info

**Date:**Mon Dec 18**Meeting Info**: 10a-11:40a, N719

**Announcement**s

- The final exam is in-class on
**Wednesday Dec 20**– see below for a list of topics/exercises to review - I will be in my office (N724) most of the day Tuesday grading your Exam #3’s. You can drop by if you want to pick up your exam, and/or go over any topics/examples for Wednesday’s final. I plan to be there 10a-3p.
- I may also have some office hours Tuesday evening over Blackboard Collaborate (time TBA)
- I reopened a few WebWork sets, as people were asking me for a chance to complete exercises they didn’t get to earlier in the semester–I reopened sets that may be useful as review for the final exam: “Substitution”, “Area Between Curves”, “Volumes of Revolution”

**Topic**s

I outlined the topics/exercises from the Final Exam Review sheet you should review for the final:

See below for a text version of this outline, which includes a list of relevant midterm and quiz exercises to review for each topic.

We went through examples of integration by parts and improper integrals:

We also introduced power series, for which we use the Ratio Test to find “the interval of convergence” (the x-values for which the given series converges). There will be an exercise on power series on the final exam, but I will count it as extra credit.

**Final Exam Review:**

Here is the annotated list of topics for the final, listed according to the exercises on the Final Exam Review sheet:

**#1(a)-(c): Integration by substitution** (see also Exam #1, exercise #4; Exam #2, exercise #1(a); Quiz #2)

**#2(a)-(c): Integration by parts** (Exam #1, exercise #5, Exam #2, exercise #1(b))

**#3(a)(b): Area between two curves** (Exam #2, exercise #3)

**#4(a)(b): Volume of solids of revolution** (Exam #2, exercises #4 & #5)

Skip #5 (Trig substitutions)

**#6(a)-(c): Method of partial fractions** (Exam #2, exercise #2; Quiz #3)

**#7(a)(b): Improper integrals** (see examples and video in Class 20 https://openlab.citytech.cuny.edu/mat1575-ganguli-fall2023/2023/11/10/class-20-recap-wed-nov-8/)

**#8: Infinite series with positive terms** (Exam #3, exercises #1-5)

**#9: Alternating series** (Exam #3, exercise #6)

**#10: Power series** (example from today’s class — see above)

Skip #10-11 (Taylor polynomials)