L’Hôpital’s Rule Guide
Resolve 0/0 and ∞/∞ limits round by round: check the form, differentiate top and bottom, repeat.
Example: (x² − 1)/(x − 1) as x → 1 is 0/0 — one round of L’Hôpital gives 2.
① Answer
② Steps
③ Why it works
L’Hôpital’s rule applies only to the indeterminate forms 0/0 and ∞/∞. The idea: near the point, the ratio of two functions heading to 0 (or ∞) behaves like the ratio of their rates of change — their derivatives. If differentiating once still leaves 0/0, you may differentiate again. If the form was never indeterminate, the rule does not apply (just substitute).