1. Section 8.2
L’Hospital’s Rule

2. Section 8.2 L’Hospital’s Rule
Learning Targets:
I can evaluate limits with indeterminate form 0/0
I can evaluate limits with other indeterminate forms.

3. L’Hospital’s Rule
Suppose that f(a) = g(a) = 0, that f and g are differentiable on an open interval I containing a, and that g’(x) is not equal to 0 on I if x is not equal to a. Then
NOTE: This is NOT the quotient rule!!

4. Example 1
Find

5. Example 2
Find

6. Example 3
Find

7. L’Hospital’s Rule can also be applied to one-sided limits! Example 4
Find

8. Indeterminate forms involving infinity Example 5
Find
SIMPLIFY!
SIMPLIFY!

9. SKIP! c) Find (Hint: Find both sides) d) Find
We need a common denominator to subtract fractions!

10. 8.2A Homework
#5, 7, 9, 11, 33, 37, 41, 49, 62,

11. Other Indeterminate Forms
Limits that lead to indeterminate forms, __________, ___________, and ____________ can be handled by taking logarithms first. Typically, taking a logarithm will lead to another indeterminate form where we can use L’Hospital’s Rule.

12. Example 6
Find
We still can’t do L’Hop because we don’t have a QUOTIENT.
REMEMBER: This is our answer for the natural log of our function…

13. Example 7 Determine whether exists and find its value if it does.
We still can’t do L’Hop because we don’t have a QUOTIENT.
REMEMBER: This is our answer for the natural log of our function…

14. Example 8
Find

15. 8.2B Homework
Complete the worksheet on pages 8-9 in your packet. and #5, 11, 33, 49; Due Monday 