advertisement

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. 1