Limits

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Descriptive Representation §

If ${\lim }_{x\to a}f(x)=L$, then the graph of $f(x)$ approaches the location of $(c,L)$. This does not mean that there is a point at $(c,L)$.

Example 1 §

$$\underset{x\to 2}{\lim }f(x)=3,f(2)=5$$

$f(x)$ has a point at $(2,5)$, but ${\lim }_{x\to 2}f(x)=3$. This means that there is a hole at $(2,3)$.

Example 2 §