How do you find the horizontal asymptote of a curve?
To find the horizontal asymptote (generally of a rational function), you will need to use the Limit Laws, the definitions of limits at infinity, and the following theorem:
Recall from the definition of limits that we can only take limits of real numbers and infinity is not a real number, which is why we need the previous theorem.
The strategy for using the theorem is to divide every term by the highest power term from the denominator; this should leave us with a polynomial in the numerator or a constant. If we have a polynomial, then there is no horizontal asymptote. If we have a constant, then y=constant is our horizontal asymptote.
We divded every term by
Now use our limit laws.
Finally use the theorem and the limit law of a constant.
So, in this case we have a horizontal asymptote of
If we ended up with
The theorem @
This is the general strategy, obviously more difficult questions can be framed and you should read your textbook for those examples.