Calculus
Lesson
16 Limits at infinity
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We have thus far only discussed horizontal tangents, but there are other times when there may be a horizontal slope: when x gets very large or very negative.
Horizontal asymptotes exist if there is a limit to the function as x goes to infinity:
is a horizontal
asymptote
Here are 3 simple cases:
1) Degree of the top polynomial is bigger than the top:
No horizontal asymptote
2) Degree of the bottom polynomial is bigger than the bottom:
Asymptote at zero
3) Degree the same:
Divide by 
and evaluate
the limit to find asymptote
Examples:
Graph each of these!!!
If a 
is involved,
then you must divide the top and bottom by 
. Note that when
, when we divide the top by 
, it is the same as dividing
by 
!!!
And graph the function.
Note that we can also say some things about some oscillating functions near infinity now:
By the Squeeze theorem (explain and draw graph), we can see that
since 
and 