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Lecture Math 141 Section 2.5 – Limits involving infinity
Two main types
I.
Taking a limit as the x goes to some value and the function goes to
e
The book calls this “infinite limits”, p. 128.
This is how we define vertical
asymptotes.
Example: Consider the function
f
(
x
) =
x
+ 3
x
2
 9
we’ll use this function
for a few ideas.
First consider the limits as the x value approaches 3
lim
x
3
x
+ 3
x
2
 9
=
Second consider the limit as the x values approach 3
lim
x
 3
x
+ 3
x
2
 9
=
Draw a preliminary graph, be sure to note what is different about
the function at the two xvalues for which you just took the limits.
II.
Taking the limit as the independent variable (usually the x) goes to to
e
The book calls this “limits at infinity” p. 131
These type help us find
horizontal asymptotes.
Example: We’ll keep working with the function
f
(
x
) =
x
+ 3
x
2
 9
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View Full DocumentConsider the limits at both
e
lim
x
x
+ 3
x
2
 9
=
lim
x

x
+ 3
x
2
 9
=
Now, draw a final graph incorporating what these limits “tell you” about the
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 Spring '07
 WEARS
 Asymptotes, Limits

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