, c^-)" />, c^+)" />, infty)" />, or -infty)" />, and suppose that lim and lim are both zero or are both , Ifhas a finite value or if the limit is , thenHistorically, this result first appeared in l"Hospital"s 1696 treatise, which was the first textbook on differential calculus" />
, c^-)" />, c^+)" />, infty)" />, or -infty)" />, and suppose that lim and lim are both zero or are both , Ifhas a finite value or if the limit is , thenHistorically, this result first appeared in l"Hospital"s 1696 treatise, which was the first textbook on differential calculus" />
Historically, this result first appeared in l"Hospital"s 1696 treatise, which was the first textbook on differential calculus. Within the book, l"Hospital thanks the Bernoulli brothers for their assistance và their discoveries. An earlier letter by John Bernoulli gives both the rule và its proof, so it seems likely that Bernoulli discovered the rule (Larson et al. 1999, p.524).
Note that l"Hospital"s name is commonly seen spelled both "l"Hospital" (e.g., Maurer 1981, p.426; Arfken 1985, p.310) và "l"Hôpital" (e.g., Maurer 1981, p.426; Gray 1997, p.529), the two being equivalent in French spelling.
L"Hospital"s rule occasionally fails lớn yield useful results, as in the case of the function
infty)u(u^2+1)^(-1/2)" />, illustrated above. Repeatedly applying the rule in this case gives expressions which oscillate and never converge,
