Indeterminate form

A limit expression like $\frac{0}{0}$ or $\frac{\infty}{\infty}$ whose value isn't determined by the form alone.

An indeterminate form is a limit expression — $\frac00$ , $\frac{\infty}{\infty}$ , $0\cdot\infty$ , $\infty-\infty$ , $1^\infty$ , $0^0$ , or $\infty^0$ — that does NOT determine the limit's actual value just from its shape. The same indeterminate form can correspond to limits equal to $0$ , to a finite nonzero number, to $\pm\infty$ , or to no limit at all, depending on the specific functions involved — the form only signals that more work (like L'Hopital's Rule or algebraic manipulation) is needed.

Examples

$\lim_{x\to0}\frac{\sin x}{x}$ has the indeterminate form $\frac00$ but equals $1$ .
$\lim_{x\to0}\frac{x^2}{x}$ also has the form $\frac00$ but equals $0$ — same form, different value.