The notion of limit

For a full and interactive version of this page with examples and exercises, check out the Pass Your Math platform!

Let \(a\) and \(b\) be real numbers and let \(f\) be a real function that is defined on an open interval containing \(a\).

We say that \(f\) has limit \(b\) at \(a\) if \(f(x)\) comes closer to \(b\) as \(x\) comes closer to \(a\).

In this case, we write \(\textstyle\lim_{x\to a} f(x) = b\) or \(\displaystyle\lim_{x\to a} f(x) = b\).

Let’s practice!

The rational function \(f(x) = \frac{2\cdot x-16}{x-8}\) is defined everywhere except at \(8\).

What is the limit of \(f\) at \(8\)?

For every value of \(x\), \(f(x)=2\) is close to (but distinct from) \(8\).


\(\lim_{x\to 8}f(x)= 2\)

Leave a Reply

Your email address will not be published. Required fields are marked *