Hospitalii regula

Hospitalii regula est regula calculi infinitessimalis pro Marchione Hospitalio nominata, qua derivativi usurpantur ad fines indeterminatas computandas.

Fertur Iohannes Bernoullius re vera regulam proposuisse, quia Marchio Ioannem pretio per annum 300 francis ad auxilium in rebus aerumnisque solvendis mathematicis dandum conduxit.^[1]

Simplicissime dictum, regula dicit in limite intervalli functionibus f(x) et g(x), si f(c)=g(c)=0 vel f(c)=g(c)=${\displaystyle \infty }$, dein:

${\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}}$

Necessitate, ${\displaystyle \lim _{x\to c}{\frac {f'(x)}{g'(x)}}}$ exstet. Sunt aliae postulationes, quae subter notantur.

• C. Truesdell The New Bernoulli Edition Isis, Vol. 49, No. 1. (Mar., 1958), pp. 54-62.

• Calculus
• Infinitas

• l'Hôpital's rule, mathworld.wolfram.com
• l'Hôpital's rule, planetmath.org