Math 413Analysis I
Final ExamSolutions
1)(15pt) Dene the following concepts:
a) (xn ) converges to L;
n=1
For all > 0 there is an N N such that |xn L| < for all n N .
b) A R is compact;
If (xn ) is a sequence of elements of A, there is a subsequence conve
Math 413 Analysis I
Midterm 1
October 17, 2003
1)(20pt) Give complete denitions of the following concepts:
a) lim f (x) = L where f : A R
xa
a is a limit point of A and for all > 0 there is > 0 such that if x A
and 0 < |x a| < , then |f (x) L| < .
b) (an
Math 413 Analysis I
Midterm 2
November 26, 2003
1)(15pt) Give complete denitions of the following concepts:
a) f : A R is continuous;
For all a A and for all > 0 there is > 0 such that if x A and
|x a| < , then |f (x) f (a)| < .
b) f : A R is uniformly co
Math 413Midterm Study Guide
The midterm exam will be on Friday October 17.
The exam will cover sections 1.3,1.4, 2.22.6, 3.13.4 and 4.2. The course
web page contains a week-by-week syllabus that gives a more detailed description of the material you are
Math 413Midterm 2 Study Guide
The midterm exam will be on Wednesday November 26.
The exam will cover sections 4.14.6, 5.15.3 . The course web page contains a week-by-week syllabus that gives a more detailed description of the
material you are responsibl