---
tag: 0S7G92KKA7
kind: concept
name: Indeterminate form
msc: [26A03]
uses: [0TXTSEMHR5, 0JWT4PPQ7B]
sources:
  - url: https://en.wikipedia.org/wiki/Indeterminate_form
    locator: List of indeterminate forms
same_as:
  wikidata: Q115089
  wikipedia: Indeterminate form
---

## Summary

An indeterminate form is a type of [[limit|0TXTSEMHR5]] where the limits of the parts do not determine the limit of the whole.
The seven common forms are $0/0$, $\infty/\infty$, $0 \cdot \infty$, $\infty - \infty$, $0^0$, $1^{\infty}$, and $\infty^0$.

## Remarks

For example, $x \to 0$ and $x^2 \to 0$, but $x^2/x \to 0$, $x/x \to 1$, and $x/x^2$ has no finite limit. All three are of the form $0/0$.
[[L'Hôpital's rule|0JWT4PPQ7B]] treats the forms $0/0$ and $\infty/\infty$. Logarithms turn the forms $0^0$, $1^{\infty}$, and $\infty^0$ into the form $0 \cdot \infty$.
Forms such as $1/0^+$ and $0^{\infty}$ are not indeterminate.

## Explanations

### L1 human

Some limits cannot be found by plugging in the limits of the parts.
Then a finer analysis is needed, because many different answers are possible.