1. MAT 1235 Calculus II Section 6.8 Indeterminate Forms and L’Hospital Rule http://myhome.spu.edu/lauw

2. Friday Quiz: 6.7, 6.8

3. Homework… WebAssign 6.8

4. Preview You have some experience with this topic from Lab 01 Definition of Indeterminate Forms When and How to apply the L’Hospital’s Rule to find limits

5. A Common Theme in calculus - Limits Some limits cannot be evaluated by simplifications and substitutions.

6. A Common Theme in calculus - Limits Some limits cannot be evaluated by simplifications and substitutions. In section 2.4, we use geometric arguments to prove that

7. A Common Theme in calculus - Limits A lot of applications We have this limit in Calculus 1-3. Used to prove the derivative of sin(x)

8. Simple Pendulum When the angle is small, the motion can be modeled by

9. Definition

11. L’Hospital’s Rule

12. Remark

13. Example 1

14. Step 1: Check that is an indeterminate form Supporting steps should be done on the right hand column.

15. Example 1 Step 2: Apply the l’Hospital’s rule

16. Remark on non-standard notation The following non-standard notation is not acceptable in this class.

17. Remark on non-standard notation The following non-standard notation is not acceptable in this class.

18. Example 2

19. Remarks For some problems, you may need to apply the rule more than once. But make sure you check the condition in step 1 every time you apply the rule.

20. Example 3

21. Q&A Q: Can I apply the l’Hospital’s rule if the limit is not in quotient form?

22. Q&A Q: Can I apply the l’Hospital’s rule if the limit is not in quotient form? A: Sometimes, we may rewrite the limit into quotient form and then apply the l’Hospital’s rule.

23. Example 4

24. Example 5

25. Example 6

26. Geometric Meanings

27. Geometric Meaning

28. Reminder: ∞ is not a number