Calculus

L'Hopital's Rule

Limits of indeterminate forms

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L=1
lim⁡x→0sin⁡xx=lim⁡x→0(sin⁡x)′(x)′=1\lim_{x\to 0}\frac{\sin x}{x} = \lim_{x\to 0}\frac{(\sin x)'}{(x)'} = 1

L'Hôpital's rule: when f(0)/g(0) = 0/0, differentiate numerator and denominator separately. The open circle shows where the value is "missing" – the limit fills it.