How do you find the horizontal asymptote of a curve?
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.
For example:
Now use our limit laws.
Now simplify.
Finally use the theorem and the limit law of a constant.
This is the general strategy, obviously more difficult questions can be framed and you should read your textbook for those examples.
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To find the horizontal asymptote of a curve, you need to determine the behavior of the curve as it approaches positive or negative infinity.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients of both the numerator and denominator. The horizontal asymptote is then given by the resulting quotient.

If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, you can have a slant asymptote in this case.
Remember that these rules apply to rational functions, which are functions in the form of f(x) = (ax^n + ...)/(bx^m + ...), where n and m are the degrees of the numerator and denominator, respectively.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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