# Final Exam Study Guide

The final exam is this Wednesday, May 20, at the usual class time. Below is an outline of topics to study, and here are some tips to how to prepare:

• Start by working through the corresponding exercises on the Final Exam Review sheet (handed out in class, also available here). Many of these were assigned as homework exercises, so you should have already worked through them.
• Also review the corresponding questions on the midterm exams. I have uploaded solutions to the exams in the Files section of the course profile.
• Of course you can also study the examples and homework exercises from the corresponding sections in the textbook.

Here is a list of topics, according to the questions in the Final Exam Review sheet:

• Final Exam Review #1: Integrating by substitution (see also Exam #1 & Sec 5.6)
• Final Exam Review #2: Integration by parts (see also Exam #1 & Sec 7.1)
• Final Exam Review #3: Using integrals to find the area between two curves (see also Exam #2 & Sec 6.1)
• Final Exam Review #4: Using integrals to find the volumes of solids of revolution (see also Exam #2 & Sec 6.3)
• Final Exam Review #5: Integrals using trigonometric Substitutions (see also Exam #2 & Sec 7.3)
• Final Exam Review #6: Integrals using the Method of Partial Fractions (see also Exam #2 & Sec 7.5)
• Final Exam Review #7: Improper Integrals (see also Exam #2 & Sec 7.6)
• Final Exam Review #8 & #9: Infinite Series (Exam #3, Sections 10/2-10.5)
• Final Exam Review #10: Power Series (Sec 10.6 – Examples 1 & 2)

# Summary of Tests for Infinite Series

I wrote up a summary of the various tests for convergence/divergence of infinite series that we discussed from Sections 10.2 and 10.3 of the text. You can use this as a reference as you do exercises, but also look at the examples in the textbook and the examples we did in class for each test:
https://openlab.citytech.cuny.edu/?get_group_doc=15883/1430748441-Math1575-InfiniteSeriesTests.pdf

UPDATE: I have extended the document to include the Alternating Series Test (Section 10.4) and the Ratio Test (Section 10.5). You can download the new version of the document here:

https://openlab.citytech.cuny.edu/?get_group_doc=15883/1431359547-Math1575-InfiniteSeriesTests-Updated.pdf

The trickiest of these is probably the limit comparison tests. It may be helpful to look at some video examples: