TABLE OF CONTENTS Because the number of results and theorems from calculus are frequently used in this book, we collect here a number of these results for ready reference, and to refresh the student s memory.
For the open interval a< x< b, we use notation (a, b), and for the closed interval a ? x ? b, we use notation [a, b].
Let a function f be defined in an open interval and L be a real number. Then for the limit of a function, we write
if for every ?>0, there is a ?>0 such that
A function f is continuous at x= a if it satisfies the following three conditions:
Note that:
A polynomial function f is continuous at each point of the real line.
If a function is continuous for all x-values in an interval, it is said to be continuous on the interval.
Let f(x) be continuous on the closed interval [a, b] then f(x) assumes its maximum and minimum values on [a, b]; that is, there are real numbers x 1, x 2 ? [a, b] such that
for all x ? [a, b].
Suppose that 
is an infinite sequence. Then the se quence is said to have the limit L, and we write
if, given any ?>0, there exists a positive integer N=N( ?) such that n>N
