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Other indeterminate forms, such as 1 ∞, 0 0, ∞ 0, 0 · ∞, and ∞ − ∞, can sometimes be evaluated using L'Hôpital's rule. We again indicate applications of L'Hopital's rule by = . For example, to evaluate a limit involving ∞ − ∞, convert the difference of two functions to a quotient:
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
The book includes the first appearance of L'Hôpital's rule. The rule is believed to be the work of Johann Bernoulli, since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300₣ per year to keep him updated on developments in calculus and to solve problems he had. Moreover, the two signed a contract allowing l'Hôpital to use Bernoulli's ...
His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his 1696 treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. [3]
L'Hôpital's rule - a method in calculus for evaluating indeterminate forms; Indeterminate form - a mathematical expression for which many assignments exist; NaN - the IEEE-754 expression indicating that the result of a calculation is not a number; Primitive notion - a concept that is not defined in terms of previously-defined concepts
1.1 limits / L'Hôpital's rule. 12 comments. 1.2 Polynomials and rational expressions. 5 comments. 1.3 Is there a specific name for this rule? 4 comments ...
See Indeterminate form. --Kinu t / c 19:34, 15 May 2016 (UTC) Indeterminate forms are quite common with +-infinity. With only real numbers (i.e. no infinities) there are only 4 indeterminate forms; 0/0, 0 to the 0, the zeroth root of 1, and the logarithm of 1 in base 1. Georgia guy 20:41, 15 May 2016 (UTC)
This rule uses derivatives to find limits of indeterminate forms 0/0 or ±∞/∞, and only applies to such cases. Other indeterminate forms may be manipulated into this form. Given two functions f(x) and g(x), defined over an open interval I containing the desired limit point c, then if: