The topic that we will be examining in this chapter is that
of Limits. This is the first of three
major topics that we will be covering in this course. While we will be spending the least amount of
time on limits in comparison to the other two topics limits are very important
in the study of Calculus. We will be
seeing limits in a variety of places once we move out of this chapter. In particular we will see that limits are
part of the formal definition of the other two major topics.
Here is a quick listing of the material that will be covered
in this chapter.
Tangent Lines and Rates of Change In this section we will take a look at two
problems that we will see time and again in this course. These problems will be used to introduce the
topic of limits.
The
Limit Here we will take a conceptual look at limits
and try to get a grasp on just what they are and what they can tell us.
One-Sided Limits A brief introduction to one-sided limits.
Limit Properties Properties of limits that we’ll need to use in
computing limits. We will also compute
some basic limits in this section
Computing Limits Many of the limits we’ll be asked to compute
will not be “simple” limits. In other
words, we won’t be able to just apply the properties and be done. In this section we will look at several types
of limits that require some work before we can use the limit properties to
compute them.
Infinite Limits Here we will take a look at limits that have a
value of infinity or negative infinity.
We’ll also take a brief look at vertical asymptotes.
Limits At Infinity, Part I In this section we’ll look at limits at
infinity. In other words, limits in
which the variable gets very large in either the positive or negative sense. We’ll also take a brief look at horizontal asymptotes
in this section. We’ll be concentrating
on polynomials and rational expression involving polynomials in this section.
Limits At Infinity, Part II We’ll continue to look at limits at infinity
in this section, but this time we’ll be looking at exponential, logarithms and
inverse tangents.
Continuity In this section we will introduce the concept
of continuity and how it relates to limits.
We will also see the Intermediate Value Theorem in this section.
The Definition of the Limit We will give the exact definition of several
of the limits covered in this section.
We’ll also give the exact definition of continuity.