Example 15
Evaluate
![](Image550.gif)
Solution : L =
![](Image551.gif)
=
=
= ![](Image554.gif)
=
[7]
= + ¥
Example 16 Evaluate
( x5 - x3 - 7x )
Solution : Let L =
( x5 - x3 - 7x )
=
![](Image557.gif)
= ![](Image549.gif)
.
![](Image559.gif)
= ![](Image560.gif)
= ![](Image549.gif) ![](Image562.gif)
L = ¥
Note:
Limits at infinity describe the behavior of functions when its independent variable increases or decreases without bound. In either cases if L is the limit
then f (x) = L or f (x) = L. (L = real number)
Also, f(x) said to have horizontal asymptote at f(x) = L.
So, in Example 12, f(x) has a horizontal asymptote at y = 1/4.
in Example 13, f(x) has a horizontal asymptote at y = 8.
in Example 14, it is y = c/2, c is a real number.
in Example 15, f(x) has no asymptote as x increases without bound.
in Example 16, f(x) has no asymptote as x decreases without bound.
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