L'Hopital's Rule
If f(x)/g(x) → 0/0 or ∞/∞, then lim f(x)/g(x) = lim f'(x)/g'(x)
Common Mistakes
- Applying L'Hopital's Rule without confirming 0/0 or ∞/∞ first — it only works for these specific indeterminate forms.
- Differentiating the whole fraction as a quotient instead of the numerator and denominator separately.
Frequently Asked Questions
Can I apply L'Hopital's Rule more than once?
Yes — if after applying it once you still get an indeterminate form, you can differentiate again and reapply the rule until it resolves.
Can L'Hopital's Rule be applied repeatedly?
Yes — if differentiating once still leaves an indeterminate form, you can differentiate the new numerator and denominator again and reapply the rule until a determinate result appears.
