1. Objective – L’Hopital’s Rule (Indeterminate Forms)
Lesson: Derivative Applications 2
Objective – L’Hopital’s Rule
(Indeterminate Forms)

3. Find the limit:

4. Indeterminate Forms – Limits of the form 0/0 or
L’Hopital’s Rule:

5. Applying L’Hopital’s Rule
Check that the limit of f(x)/g(x) is an
indeterminate form of 0/0 or
2. Differentiate f and g separately
3. Find the limit of f’(x)/g’(x). If this limit is
finite, + infinity, or – infinity then it is equal
to the limit of f(x)/g(x).

6. EX 1: Find the limit using L’Hopital’s Rule.

7. Why does L’Hopital’s Rule Work?
Basically, since , it is considered
to be in indeterminate form. (Meaning other
methods must be used to evaluate it).
We will be using a tangent line approximation
to approach the limit value.

8. If f and g are continuous & diff. at x = a, then:
also
so,

9. EX. 2: In each part, confirm that the limit is
an indeterminate form and evaluate it
using L’Hopital’s Rule

10. Ex. 3: Evaluate the limit
Let’s try L’Hopital’s rule:

11. Therefore, L’Hopital’s rule doesn’t apply