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