Math 252a Exam 3 Spring 2024

Exam will be Wednesday, April 17, in KELLER 402 (12:30-1:20) and KELLER 401 (1:30-2:20)

• The exam covers: 11.1-11.10 (excluding Taylor remainders in 11.10)
• A large chunk of the exam will consist of a number of sequences and series which you will test for convergence. There will generally be no instructions as to which test to use - you will have to figure that out yourself. For the series that have negative terms, you should check for absolute convergence as well as conditional convergence.
• You will also need to understand the difference between a sequence and a series, and what the relation between the two are.
• You can also expect to compute one or two series exactly (for example, a geometric or telescoping series).
• For power series, you will need to find the radius and interval of convergence, and either the series corresponding to a function or the functions corresponding to a series (or both), ie section 11.9 problems.
• There will be at least one Taylor Series problem, asking you to find the nth Taylor polynomial for a function. Taylor remainders will not be on this exam, though you might need to estimate an error some other way (for example, if the corresponding series is alternating).
• You can expect some slightly theoretical problems about sequences and/or series. and one problem estimating an error from estimating a series from a finite sum. These might be the same problem.
• Most of the problems will be similar to text problems, so you should review the homework, maybe look at problems near ones that were assigned. Here are some more, from the review section:
  • p.824 Tre-False section/Look at all of these, they're really good problems! Most should just take you a few seconds.
  • p. 825-826/Easy ones: 3,5,7, 11, 13, 17, 27, 31, 32, 34, 35, 47
  • p. 825-826/Somewhat harder ones: 9, 21, 22, 25, 28, 36, 38, 39, 41, 43, 44, 45, 55, 59
• As always, you will not be allowed to use a calculator, and you will be allowed to use a crib sheet consisting of one side of one 8x11 sheet of paper with whatever you care to put on it.
• I will probably give you Table 1 from 11.10, but that's it as far as formulas.