How do I find the limits of rational functions?

There are various methods (which you will employ in Precalculus) for determining a limit.

First, you could attempt direct substitution.

If that doesn't work, attempt these approaches:

To find out which approach they want you to use, you have to carefully read the instructions.

I hope this is useful.

To find the limits of rational functions:

1. Simplify the rational function if necessary.
2. Determine the behavior of the function as it approaches the given point (usually infinity or a specific real number) by analyzing the degrees of the numerator and denominator.
3. Apply the rules for limits of rational functions:
   • If the degree of the numerator is less than the degree of the denominator, the limit is 0.
   • If the degree of the numerator equals the degree of the denominator, the limit is the ratio of the leading coefficients.
   • If the degree of the numerator is greater than the degree of the denominator, the limit is either infinity, negative infinity, or does not exist.
4. If necessary, use techniques such as factoring, rationalizing the numerator or denominator, or applying L'Hôpital's Rule to simplify the function further before evaluating the limit.