Homework 6
Math 311, Spring 2009
Note: problems with (*) are harder ones. (17.1) see back of book (17.8) (a) consider two cases of f g and f < g; (b) use min(f, g) = (f + g)/2 |f g|/2 and max(f, g) = (f + g)/2 + |f g|/2; (c) Use 17.3 and 17.4. (17.9d) Ass
Quiz 1 solution
Math 311
1. (3 pts) Prove that 3 is irrational. 5 6. Proof 1:Suppose that x = 2 + 3 is rational. Then x2 is also rational, which is + 2 2 - 5 = 2 6, then (x2 - 5)2 = 24, or equivalently x4 - 10x2 + 1 = 0. Thus Since x 2+ 3 is a root of the
Quiz 3
Math 311
Name: Total Score: 10 pts
1. (3 pts) Use denition to prove that f (x) = 2/(1 + x) is continuous at x = 3. 2 1 We need to prove: > 0, > 0, such that |x 3| < implies that < . 1+x 2 3x 2 1 = , If we choose |x 3| < 1, we will have 2 < x < 4 No
Quiz 2 solution
Math 311
Name: 1 , if n is odd; 1. (3 pts) Define an = n + 1 n , if n is even. n+1
Total Score: 10 pts
.
(a) Find lim inf an and lim sup an ; (you do not need to prove) (b) Find supcfw_an and infcfw_an (you do not need to prove). lim inf
HOMEWORK #2, DUE THURSDAY, September 10, IN CLASS
(*) You may work in teams of size no more than three. Each team should hand in a single homework
set, signed by all of the teams members. All team members will receive the same score for this
homework. The