L’Hospital’s Rule
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- L’Hospital’s Rule
For any indeterminate limit,
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Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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L’Hospital’s rule
L’Hospital’s rule can evaluate certain quotient limits with the indeterminate forms 0/0 or infinity divided by infinity. Its hypotheses require appropriate differentiability near the target, a nonzero denominator derivative there, and a suitable limit of the derivative quotient. For example, lim(x→0) sin x/x equals lim(x→0) cos x/1=1. Differentiating numerator and denominator separately here is a limit theorem, not the quotient rule for derivatives.