1. Warm-up
A rancher has 200 feet of fencing with which to enclose 2 rectangular corral (see picture). What dimensions should be used so the enclosed area will be a maximum?

2. 23. Section 4.7 L’Hopital’s Rule

3. L’Hopital’s Rule
EQ – When is L’Hopital’s rule used?

4. L’Hopital’s Rule
L’Hopital (Lo-pee-tal) was french mathematician who wrote the first calculus textbook
L’Hopital’s rule is used to evaluate limits of certain types of quotients of two functions
If the quotient has an indeterminate form , you can replace with

5. Caution!
You need to be careful to take derivatives of numerator and denominator separately! Do not use the quotient rule!!

6. Example
Use L’Hopital’s rule to evaluate

7. Example
Use L’Hopital’s rule to evaluate

8. Example
Use L’Hopital’s rule to evaluate

9. Example
Use L’Hopital’s rule to evaluate

10. Example
Use L’Hopital’s rule to evaluate

11. Example Use L’Hopital’s rule to evaluate If you get 00, then take ln
Now exponentiate (undo the ln)

12. Comparing Growth of Functions
We say f(x) grows faster than g(x) if

13. Example Which grows faster? Therefore f(x)=x2 grows faster
Write this as

14. Assignment
Pg. 277: #1-19 odd, 27, 31, 43, 49, 59