Math 314 Fall 2013 Midterm Solutions
Oct. 24, 2013 2pm  3:20pm. Total 25 Pts
NAME:
ID#:
Please write clearly and show enough work.
No electronic devices are allowed.
Question 1. (4 pts) A sequence of functions cfw_fn(x) is said to converge
uniformly on E
Math 314 Fall 2013 Homework 1 Solutions
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. The Fibonacci numbers are dened through
f1 = 1, f2 = 1, f3 = 2,
(1)
fn = fn1 + fn2
(
Math 314 Fall 2013 Homework 6 Solutions
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. Let f (x) = x. Prove by denition that f (x) is a continuous function (that is f (x
Math 314 Fall 2012 Midterm Practice Problems Solutions
Oct. 19, 2012
To best prepare for midterm, also review homework problems.
To get most out of these problems, clearly write down (instead of mumble or think)
your complete answers (instead of a few lin
Math 314 Fall 2012 Final Practice
You should also
review homework problems.
try the 2011 nal (and you should feel most of its problems are easy).
Most problems in the nal will be at the Basic and Intermediate levels (First 36
problems).
Basic
Problem 1. L
Math 314 Fall 2012 Midterm Review
Oct. 18, 2012
Warning: This is not a complete list of materials covered by the midterm. You still need to read the
notes, review homeworks, and work on practice problems.
1. Logic
Logic: Understand the meaning of and, or,
Math 314 Fall 2013 Homework 9 Solutions
Due Wednesday Nov. 20 5pm in Assignment Box (CAB 3rd Floor)
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. Let a > 0. Use Mean Valu
Math 314 Fall 2013 Homework 2 Solutions
Due Wednesday Sept. 25 5pm in Assignment Box (CAB 3rd Floor)
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. Let E R. Prove that (E

2. Sets in R
2.1. Sup and Inf.
2.1.1. Denitions.
Denition 2.1. (sup and inf) Let A be a nonempty set of numbers. The supreme of A is dened as
sup A = min cfw_b R: b
If cfw_b R: b
a for every a A.
(2.1)
a for every a A = , we write
sup A = ;
(2.2)
The in
Math 314 Fall 2013 Homework 5 Solutions
Due Wednesday Oct. 16 5pm in Assignment Box (CAB 3rd Floor)
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. Let cfw_xn = cfw_x1, x2
1. R
In this and the next section we are going to study the properties of sequences of real numbers.
Denition 1.1. (Sequence) A sequence is a function with domain N.
Example 1.2. A sequence of real numbers is a function with domain N and range R. We will

3. Real Functions and Continuity
A real function is a function with domain R and range R.
3.1. Limits of Real Functions.
3.1.1. Denition.
Consider a real function f (x). We would like to understand its limiting behavior toward a point x0, that
is, we wo
Math 314 Fall 2013 Homework 10 Solutions
Due Wednesday Nov. 27 5pm in Assignment Box (CAB 3rd Floor)
There are 6 problems, each 5 points. Total 30 points.
Please justify all your answers through proof or counterexample.
Question 1. Let
f (x) =
1 x=1
.
0 x