L'Hôpital's Rule: if lim f(x)/g(x) is 0/0 or ±∞/±∞, then lim f(x)/g(x) = lim f'(x)/g'(x) (if the latter exists). Can apply repeatedly until form resolves. Named after Guillaume de l'Hôpital but discovered by Johann Bernoulli.
How to Use
Select a limit problem:
- f(x) / g(x): Choose numerator and denominator
- Point: Where to evaluate
- Output: Step-by-step resolution
Indeterminate Forms
- 0/0 — direct L'Hôpital
- ∞/∞ — direct L'Hôpital
- 0·∞ — rewrite as 0/(1/∞)
- ∞−∞ — combine fractions
- 0⁰, 1^∞, ∞⁰ — take log
Common Pitfalls
Only use when the form IS indeterminate. Applying to non-indeterminate forms gives wrong answers. Also, the rule can cycle infinitely (e.g., sin(x)/cos(x) at infinity).
Step-by-Step Instructions
- 1Select a preset or enter functions.
- 2Set the limit point.
- 3Check indeterminate form.
- 4View differentiation steps.
- 5Get the final limit.