MathLiveL'Hôpital's rule
When a limit of a quotient of two functions gives an indeterminate form such as 0/0 or infinity/infinity, the limit of the quotient equals the limit of the quotient of their derivatives. It is used to evaluate such limits when direct substitution fails.
\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}What the symbols mean
| numerator function | |
| denominator function, with g(x) nonzero near a | |
| derivative of f with respect to x | |
| derivative of g with respect to x | |
| point (or infinity) that x approaches |
About this formula
- FieldMathematics
- TopicLimits and derivatives
- LevelUniversity
- Also calledBernoulli-L'Hôpital's rule, limit of a fraction using derivatives, indeterminate form 0/0 limit, derivative rule for limits, L'Hospital's rule
- SourceWikidata Q190557
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “l'hôpital's rule”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.