Math 414: Analysis I
Exam 2 Topics
1. Sequences (including what it means for a sequence to be bounded/unbounded),
Definition of lim(xn ) (See in book: 2.1.1–2.1.7, , HW 4: #3#4)
2. Monotone Sequences, Monotone Convergence Theorem (See in book: 2.1.9–2.1.12,
HW 4: #2 )
3. Subsequences (See in Book: 2.1.14, 2.1.15, 2.1.17, HW 4: #1)
4. Limit Laws Associated with Sequences, Squeeze Theorem (See in Book: 2.2.1–2.2.7,
HW 5: #1–#5)
5. Limit superior, limit inferior, Bolzano-Weierstrass Theorem (See in Book: 2.3.1–
2.3.5, 2.1.13, 2.3.14, HW 5: #6)
6. Properly Divergent Sequences (HW 6: #3,#4,#5)
7. Cauchy Sequences (See in book: 2.4.1, 2.4.2, 2.4.4, HW 6: #6–#9)
8. Series (See in book: 2.5.1–2.5.4, 2.5.11)
Additional Details
• Exam 2 will occur in class on Friday, March 14 in our usual classroom.
• In addition to going over the homework, please refer to the examples done in class,
as parts of the exam may resemble these examples.
• Although you have 50 minutes to complete the exam, I will be in the classroom at
10:55 AM for those who would like extra time. The exam will conclude at 11:05
AM.
• No notes or electronic devices may be used on the exam.
• Format of the Exam: The first question will involve true/false questions similar
to your first exam (See Problem 3 on Exam 1). For the remainder of the exam you
may pick 3 problems out of the 4 problems available. If you do all 4 problems, I
will use your 3 highest grades. The rest of these problems are weighted equally.
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