L'Hôpital's Pronunciation:
We pronounce this as Lo-pitalL'Hopital's Rule Definition:
The limit of a quotientequals
limit of derivative of quotients.We use L'Hôpital's Rule for:
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 |
Since the limit is indeterminate
we can use L'Hôpital's Rule
Taking the limit as x goes to 3:
| ƒ'(x) | |
| g'(x) |
| ƒ'(x) | |
| g'(x) |
| ƒ'(x) | |
| g'(x) |
limx → 3 ƒ'(x)/g'(x) = 108
Other Resources:
limit of a function lessonderivative calculator
How does the L'Hôpital's Rule Calculator work?
Free L'Hôpital's Rule Calculator - This lesson walks you through L'Hôpitals's Rule including the definition, pronunciation, notation, and examples
What 1 formula is used for the L'Hôpital's Rule Calculator?
limx → c ƒ(x)/g(x) = limx → c ƒ'(x)/g'(x)For more math formulas, check out our Formula Dossier
What 8 concepts are covered in the L'Hôpital's Rule Calculator?
constanta value that always assumes the same value independent of how its parameters are variedderivativerate at which the value y of the function changes with respect to the change of the variable xexponentThe power to raise a numberfractionhow many parts of a certain size exista/b where a is the numerator and b is the denominatorfunctionrelation between a set of inputs and permissible outputs
ƒ(x)limitthe value that a function (or sequence) approaches as the input (or index) approaches some valupowerhow many times to use the number in a multiplicationvariableAlphabetic character representing a number
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