Indeterminate form

Summary

An indeterminate form is a type of limit 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 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.

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L'Hôpital's rule

Tag	`0S7G92KKA7`
URI	`m2://0S7G92KKA7`
Kind	concept
Writing	W1 stated
MSC	26A03
Uses	Limit of a function
Same as	Wikidata Q115089 Wikipedia Indeterminate form

Indeterminate form

Summary

Remarks

Reading path

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Further reading

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