Evaluating lim(x→0) sin(x)/x Using L'Hôpital's Rule

Calculus 1 · Axiom Academy

EXAMPLE L'Hôpital's Rule on sin(x)/x A classic 0/0 limit, worked one step at a time with L'Hôpital's Rule. Evaluate the limit . Decide whether L'Hôpital's Rule applies, and if so, use it to find the value. Nicely done. You confirmed a form, applied L'Hôpital's Rule, and read off the value. Check first: L'Hôpital's Rule only applies to an indeterminate form like or — here . Differentiate separately: replace numerator and denominator with their own derivatives, and — this is not the quotient rule. The takeaway: spot the indeterminate form, differentiate top and bottom, and re-evaluate — and remember which results rest on which.

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