L'Hospital's Rule
Let lim stand for the Limit 
, 
, 
, 
, or
, and suppose that lim 
and lim 
are both Zero or are both 
. If
has a finite value or if the Limit is
, then
L'Hospital's rule occasionally fails to yield useful results, as in the case of the function
. Repeatedly applying the rule in this case gives expressions which oscillate and never converge, |  |  | |
|  | ||
|  |
(The actual Limit is 1.)
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 13, 1972. L'Hospital, G. de L'analyse des infiniment petits pour l'intelligence des lignes courbes. 1696.
- Abel's Inequality
- Abel's Irreducibility Theorem
- Abel's Lemma
- Abel's Test
- Abel's Theorem
- Abel's Uniform Convergence Test
- Abel Transform
- Abhyankar's Conjecture
- Ablowitz-Ramani-Segur Conjecture
- Abscissa
- Absolute Convergence
- Absolute Deviation
- Absolute Error
- Absolute Geometry
- Absolutely Continuous
- Absolute Pseudoprime
- Absolute Square
- Absolute Value
- Absorption Law
- Abstraction Operator
- Abundance
- Abundant Number
- Acceleration
- Accidental Cancellation
- Accumulation Point