1. Welcome Back!
April 24, 2007

2. Indeterminate Forms and L’Hopital’s Rule Part 2
Chapter 4.4
April 2007

3. Indeterminate Forms
Any limit of the form is called an indeterminate form of type
We call the form an indeterminate form of type
Other Indeterminate forms are:

4. L’Hopital’s Rule applies ONLY to indeterminate forms:
If the Or
Provided the limit on the right exists (or is or )
Then
Take for example:
Indeterminate form:

5. However we can manipulate expressions of other forms so they fit the criteria:
The form is:
L’Hopitals does not apply, but if we rewrite the limit as
the resulting form will be or
And we can apply L’Hopital’s Rule.

6. However we can manipulate expressions of other forms so they fit the criteria:
The form is:
L’Hopitals does not apply, but if we rewrite the limit as a quotient (finding a common denominator) the resulting
form will be or
And we can apply L’Hopital’s Rule.

7. Example:
The form is:
L’Hopitals does not apply, but we can combine the log term using properties of logs:
Which gives us the form

8. The last forms involve exponents and we’ll use these properties of logs: in our solution.
The form is:
L’Hopitals does not apply, but if we rewrite the function in terms of e using the first property of logs:
We can use the second property and find the limit using our previous forms.

9. More Examples: