Vocabulary
limit at infinity, infinite limit,
horizontal asymptote, indeterminate expression, infinite limit at infinity
Objectives
1.
Explain what is meant by equations such as
or .
2.
Recognize indeterminate expressions.
3.
Sketch the graph of a function with specified limit conditions.
4. Find
the value of certain limits at infinity and infinite limits.
5.
Determine the horizontal and vertical asymptotes of a given function.
Lecture Outline
In this section we consider the end
behavior of functions. That is, we examine the behavior of as
increases without bound or decreases without bound.
Definition of Limit at Infinity
Let
be a function which is defined on some interval ( ). Then
means that the values of can be
made arbitrarily close to by taking sufficiently large.
Often when is a rational function, the graph of will behave like a line as increases or decreases without bound. When
this happens, the line which the graph of
approaches is called a horizontal asymptote .
