Principles of Analysis

Homework Assignment #5

Due Friday, October 18, 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:   1a, 1c, 1e, 4 (both parts), 9

Hint: For problem #1, divide top and bottom of the fraction by the "highest" power. For problem #9, why can't you simply apply the Big Limit Theorem?

Section 2.3
Problems:   2a, 2b, 3, 5a, 10

Hint: For problem #2, as usual with True/False questions, if the statement is true give a proof, otherwise give a counterexample. For problem #5a, you are proving the other half of Theorem 2.3.1. Try converting the decreasing sequence {x_n} into an increasing sequence {y_n} with a simple arithmetical operation.

Section 2.4
Problems:   1b, 1d, 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.