Tuesday, June 30, 2015

Advanced Math Solutions – Limits Calculator, Rational Functions

In the previous post, we learned how to find the limit of a function with a square root in it. Today we will be dealing with rational functions, which are handled differently than the function in the previous posts because rational functions follow a set of rules. A rational function is a function with a ratio of two polynomials, F(x)=\frac{P(x)}{Q(x)}.

Here are the rules:
  1. If the degree of P(x) is less than the degree of Q(x), then the limit is 0.
  2. If the degree of P(x) and Q(x) are the same, then divide the coefficients of the terms with the largest exponent to get the limit.
  3. If the degree of P(x) is greater than the degree of Q(x), then the limit is either \infty or -\infty depending on the signs of polynomials. If both the coefficients of the largest exponent are either negative or both positive, then the limit is \infty. Otherwise, the limit is -\infty.

Here is an example of Rule 1 (click here):

Here is an example of Rule 2 (click here):

Here is an example of Rule 3 (click here):

Rational functions are easy to solve as long as you remember those three rules. Next post, we will talk about L’Hopital’s rule.

Until next time,


  1. Thank you for another essential article. I have learned a lot from your article.I like mathematic. Thank so much, again.

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  4. Just a little confusion why we apply infinite properties, other than that, understands the whole part. Thanks for solving it in a simpler and wiser way.
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