# The notion of limit

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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) $$8$$.

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