Example · High school
Terms
| Term | This example | Why |
|---|
| limit (of a function) |
$\lim_{x \to 0} f(x) = 1$
|
$f(0)$ is undefined, but the limit exists anyway.
|
| left limit |
$\lim_{x \to 0^{-}} f(x) = 1$
|
|
| right limit |
$\lim_{x \to 0^{+}} f(x) = 1$
|
$\frac{\sin x}{x}$ approaches $1$ from both sides of $0$, so the left limit, the right limit, and the limit are all $1$, even though $f(0)$ is undefined.
|
| continuous |
✗ |
The function is not continuous at $x = 0$ because $f(0)$ is undefined, so $x = 0$ is not in the domain of $f$.
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