1. L’Hospital’s Rule
Lesson 4.5

2. Problem
There are times when we need to evaluate functions which are rational
At a specific point it may evaluate to an indeterminate form

3. Example of the Problem Consider the following limit:
We end up with the indeterminate form
Note why this is indeterminate

4. L’Hospital’s Rule
When gives an indeterminate form (and the limit exists)
It is possible to find a limit by
Note: this only works when the original limit gives an indeterminate form

5. Example
Consider As it stands this could be
So we claim

6. This is not an indeterminate result
Example
Consider
Why is this not a candidate for l’Hospital’s rule?
Note also example 7, pg the limit must exist
This is not an indeterminate result

7. Example Try When we apply l’Hospital’s rule we get
We must apply the rule a second time

8. Hints Manipulate the expression until you get one of the forms
Express the function as a fraction to get

9. Assignment
Lesson 4.5
Page 236
Exercises 1 – 55 EOO