L'Hôpital's rule

L'Hôpital's rule is a mathematical rule that can calculate limits of an indeterminate form using derivatives. When the rule is used (it can be used multiple times), it turns an indeterminate form into a value that can be solved.

L'Hôpital's rule states that for functions $f$ and $g$ which are continuous over an interval, if $\lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0{\text{ or }}\pm \infty$ and $g'(x)\neq 0$ and $\lim _{x\to c}{\frac {f'(x)}{g'(x)}}$ exists, then

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

When the rule is used, it usually simplifies the limit or changes it to a limit that can be solved.

Calculus
Precalculus	Binomial theorem Concave function Continuous function Factorial Finite difference Free variables and bound variables Graph of a function Linear function Radian Rolle's theorem Secant Slope Tangent
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Miscellaneous topics	Complex calculus Contour integral Differential geometry Manifold Curvature of curves of surfaces Tensor Euler–Maclaurin formula Gabriel's horn Integration Bee Proof that 22/7 exceeds π Regiomontanus' angle maximization problem Steinmetz solid