Lesson 15 of 18Article15 min
L'Hôpital's Rule & Indeterminate Forms
If lim f/g yields 0/0 or ∞/∞ and the derivatives cooperate, lim f/g = lim f′/g′ (when the latter exists). Reapply if needed; rewrite other forms (0·∞, ∞−∞, 1^∞, 0⁰, ∞⁰) into quotients first.
When substitution gives 0/0 or ∞/∞
If lim f/g yields 0/0 or ∞/∞ and the derivatives cooperate, lim f/g = lim f′/g′ (when the latter exists). Reapply if needed; rewrite other forms (0·∞, ∞−∞, 1^∞, 0⁰, ∞⁰) into quotients first.
- Classic: limₓ→0 sin x / x = lim cos x / 1 = 1.
- Does not apply to 1/0-type forms — fix algebra first.
- Still prefer algebraic simplification when it is easier than differentiating.