Principles of Analysis

Homework Assignment #5

Due Friday, March 1, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

Section 2.2
Problems:   1d, 1e, 4 (both parts), 9

Hint: For problem #1, divide top and bottom of the fraction by the "highest" power.

Section 2.3
Problems:   2a, 2b, 3, 5 (both parts), 10

Hint: For problem #5, you are proving the other half of Theorem 2.3.1. For part (a), convert the decreasing sequence {x_n} into an increasing sequence {y_n} with a simple arithmetical operation. Then apply the result proved in class that a bounded increasing sequence converges. For part (b), use the definition of convergence and mimic the proof for bounded increasing sequences done in class.

Section 2.4
Problems:   1b, 1c, 1e, 4, 5b, 7a, 7b, 7c

Hint: For problems #1 and #7, start writing down the terms of the sequence and look for a familiar pattern.