infinite limit

A limit that grows without bound — the function's outputs increase or decrease without settling on a number.

We write $\displaystyle\lim_{x\to a} f(x) = \infty$ (or $-\infty$ ) when $f(x)$ grows without bound as $x \to a$ . This is a description of behavior, not an actual limit value — the limit still fails to exist in the ordinary sense.

Examples

$\displaystyle\lim_{x\to 0^+} \dfrac{1}{x} = \infty$ .