L'Hôpital's Pronunciation:
We pronounce this as Lo-pital
L'Hopital's Rule Definition:
The limit of a quotientWe use L'Hôpital's Rule for:
equals
limit of derivative of quotients.
indeterminate limits of quotients
0/0, or ∞/∞
L'Hopital's Rule Notation:
limx → c ƒ(x)/g(x) = limx → c ƒ'(x)/g'(x)L'Hopital's Rule Example:
| ƒ(x) = | x4 - 81 |
| x - 3 |
Taking the limit as x goes to 3:
| 34 - 81 | |
| 3 - 3 |
| 81 - 81 | |
| 0 |
| 0 | |
| 0 |
Since the limit is indeterminate
we can use L'Hôpital's Rule
Taking the limit as x goes to 3:
Other Resources:
limit of a function lessonderivative calculator