1. Indeterminate Forms and L’Hopital’s Rule

2. In evaluating functions often you need to know how a function behaves near a number
is undefined at x = 1
Need to know how it behaves near 1
Called an Indeterminate for of type 0/0

3. Indeterminate form of type ∞/∞

4. L’Hopital’s Rule
If f and g are differentiable and g’(x)≠0 near a, then May use more than once if necessary

5. DO NOT APPLY L’Hopital’s Rule unless an Indeterminate form is produced
For instance, the following application of L’Hôpital’s Rule is incorrect.
The reason this application is incorrect is that, even though the limit of the denominator is 0, the limit of the numerator is 1, which means that the hypotheses of L’Hôpital’s Rule have not been satisfied.

6. Practice
Find the following limits 1) 2)

7. 3) 4) 5)