L'Hôpital's rule

Mathematical rule for evaluating limits

L'Hôpital's rule ( loh-pee-TAHL), also known as Bernoulli's rule, is a mathematical theorem used for evaluating the limit of a quotient of two functions, each of which tends to zero or infinity, by taking each function's derivative. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital, who published it in his 1696 textbook after learning it from his tutor, the Swiss mathematician Johann Bernoulli. For two functions f {\displaystyle f} and g {\displaystyle g} , under most circumstances the limit of their quotient can be evaluated as the quotient of the limits: lim x → c f ( x) / g ( x) = {\textstyle \lim _{x\to c}f(x)/g(x)={}} lim x → c f ( x) / lim x → c g ( x) {\textstyle \lim _{x\to c}f(x){\big /}\lim _{x\to c}g(x)} .

From Wikipedia, under CC BY-SA. More on occurri.