Math 3000 Final Review Sheet
My advice for preparing for the nal exam:
First go over all three exams and make sure you can do every problem. If I thought it was
important enough to be an exam, I might think it important enough to be on the nal. It is best
Math 3000 Homework
Prove the following using the - denition of limit. Do not use properites of limits. Assume
that f : A R where A R is the largest possible domain for the given formula.
1. Prove lim (x2 + 3x + 1) = 11.
x2
2. Prove lim (5x2 + 2x + 3) = 6.
Topics covered on Exam 3
Bolzano-Weierstrass Theroem know the statement and be familiar with the proof
Nested Interval Theorem know the statement and be familiar with the proof
Definition of a relation between two sets
Definition of function in terms of r
Math 3000 Homework
In topology there is a concept called connected. The denition is that a set S is connected if for
any cover of S by two open sets U and V , with the property that S U V = , one of the sets
(either U or V ) must contain every point in S