o level maths limits

Limits

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 Mean 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.