1. Journal
A few to practice Don’t forget FRF!!!!!

2. Limit Review and L’Hopital’s Rule
Calculus BC Unit 3 Day 4
Limit Review and L’Hopital’s Rule

3. Practice: Find the following Limits

4. Journal
A few to practice Don’t forget FRF!!!!!

5. Limit
Remember: A tells us what a function’s y-values are doing as we APPROACH an x-value.

6. Types of determinate limits from plug in
Value:
Infinity

7. Types of determinate limits from plug in
3. Zero

8. Summary of Limit Forms
Determinate

9. What to do for this case? Direct substitution leads to :
An INDETERMINATE form

10. Indeterminate Form Maybe it’s zero Maybe it’s infinity or undefined
Maybe it’s some other number
We don’t know…yet

11. L’Hopital’s Rule
If f(a)=g(a)=0 AND and f’(a) and g’(a) exist
then

12. Back to our problem

13. Back in AB Calculus . . . . Graphically we could tell that
Today we can show this analytically using
L’Hopital’s Rule.
FIRST check to see that L’H can be applied!!

14. You Try

15. L’Hopital’s Rule
Also applies to
Another indeterminate form

16. Remember when using L’Hopital’s Rule:
Always check for an indeterminant form!
Calculate
Indeterminant form?

17. More Limits to ∞

18. Indeterminate Forms:
L’Hopital Applies. An indeterminate form could be in disguise:
Rewrite as a division problem.
Khan Academy
Khan Academy

19. Strategy we used: Rewrite multiplication as division
An incognito indeterminate form.
We need to transform it to be familiar.
Now we can use L’H
Strategy we used: Rewrite multiplication as division

20. Other things to remember about Limits
If then x=a is a Vertical Asymptote If then y=b is a Horizontal Asymptote