AP Calculus AB and BC glossary

Indeterminate form

Also called: 0/0

An indeterminate form is a limit expression whose value cannot be determined from its form alone, such as zero over zero or infinity minus infinity. It is not an answer but a signal that you need algebra or L'Hopital's rule to resolve the limit.

The seven indeterminate forms are $\frac{0}{0}$ , $\frac{\infty}{\infty}$ , $0 \cdot \infty$ , $\infty - \infty$ , $1^{\infty}$ , $0^0$ , and $\infty^0$ . Each can produce any value depending on the specific functions involved, which is exactly why the form alone decides nothing.

Forms like $\frac{1}{0}$ and $\frac{\infty}{0}$ are not indeterminate. They tell you the limit is infinite, which is a definite conclusion about how the limit fails to exist.

The mistake

Writing $\frac{0}{0} = 1$ or $\frac{0}{0} = 0$ . Getting an indeterminate form means you have learned nothing yet, not that you have found the answer.

Appears in: Unit 1: Limits and Continuity, Unit 4: Contextual Applications