 # L'Hôpital's Rule

## L'Hôpital's Pronunciation:

We pronounce this as Lo-pital

## L'Hopital's Rule Definition:

The limit of a quotient
equals
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

 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:

 ƒ'(x) g'(x)
 =
 4x3 1

 ƒ'(x) g'(x)
 =
 4 * 33 1

 ƒ'(x) g'(x)
 =
 4 * 27 1

limx → 3 ƒ'(x)/g'(x) = 108

## Other Resources:

limit of a function lesson
derivative 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?

1. 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?

constant
a value that always assumes the same value independent of how its parameters are varied
derivative
rate at which the value y of the function changes with respect to the change of the variable x
exponent
The power to raise a number
fraction
how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
function
relation between a set of inputs and permissible outputs
ƒ(x)
limit
the value that a function (or sequence) approaches as the input (or index) approaches some valu
power
how many times to use the number in a multiplication
variable
Alphabetic character representing a number