M3210-1 Third Homework Assignment

MATH 3210 § 1 THIRD HOMEWORK ASSIGNMENT Due Friday,

A. Treibergs September 12, 2008.

MATH 3210 § 1	THIRD HOMEWORK ASSIGNMENT	Due Friday,
A. Treibergs		September 12, 2008.

A. Please hand in the following problems from Mattuck's Introduction to Analysis.

415 [ 7, 10 ]

B. Please hand in the following problems from Taylor's Foundations of Analysis.

14 [ 9, 11, 14 ]

C. Please hand in the following additional problem.

Let x₀ = 2 and x_n+1 = 3 - 1 / x_n for all n ≥ 0.

Show: 2 ≤ x_n ≤ 3 for all n;

Show that the sequence is increasing: x_n+1 ≥ x_n for all n.

A. Please hand in the following problems from Mattuck's Introduction to Analysis. 415 [ 7, 10 ]
B. Please hand in the following problems from Taylor's Foundations of Analysis. 14 [ 9, 11, 14 ]
C. Please hand in the following additional problem. Let x₀ = 2 and x_n+1 = 3 - 1 / x_n for all n ≥ 0. Show: 2 ≤ x_n ≤ 3 for all n; Show that the sequence is increasing: x_n+1 ≥ x_n for all n.