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L'Hôpital's rule

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• L'Hôpital's Rule,l'Hôpital's Rule,l'Hôpital's rule
• L'Hospital's rule
• rule of L'Hôpital,rule of l'Hôpital

Named after French mathematicianGuillaume de l'Hôpital (1661–1704).

• IPA^(key):/ˌloʊpiːˈtɑːlz ˈɹuːl/^[1]

L'Hôpital'srule

1. (mathematics) Therule that thelimit of the ratio of two functions equals the limit of the ratio of theirderivatives, usable when the former limit isindeterminate and the latter limit exists.

In mathematical terms,${\displaystyle \underset{x\to a}{lim}\frac{f(x)}{g(x)}=\underset{x\to a}{lim}\frac{f^{\prime }(x)}{g^{\prime }(x)}}$. The rule is applicable if the former limit turns out to be${\displaystyle \frac{0}{0}}$ or${\displaystyle \frac{\mathrm{\infty }}{\mathrm{\infty }}}$ and requires that the latter limit exist (including that${\displaystyle g^{\prime }(x)\ne 0}$ for all${\displaystyle x\ne a}$ in some interval around${\displaystyle a}$).

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