2. Warm up

3. POP QUIZ!

4. Pop Quiz Using f & g, graphically find the limits for #1-6. f(x) g(x)

5. Pop Quiz Algebraically, find the limit of each in #7-10

6. Answers 1. 2 2. 1 3. DNE 4. 4 5. 0 6. DNE 7. 3/2 8. 1/3 9. 3 10. 1

7. Section 2.3 Calculating Limits Using the Limit Laws SWBAT SWBAT –Calculate limits using limit laws

8. Direct Substitution Property (Review) Let’s start with the following: Let’s start with the following: If you can evaluate the limit at a, then do it. If you can evaluate the limit at a, then do it. This is also known as “Plug and Chug” This is also known as “Plug and Chug”

9. Simplify with algebra: Remember this? Remember this? This is called an Indeterminate form This is called an Indeterminate form (it can not be determined) (it can not be determined) Now plug and chug!:Now plug and chug!: The limit is 3The limit is 3 Plug and chug. Plug and chug. You get 0 / 0 You get 0 / 0

10. The Limit Laws (don’t write this down)

12. Further Limit Properties (if you think it would help you, then writ it down, if not they are on p. 109) Applying the Product Law repeatedly with g(x) = f(x) gives the following Power Law: Applying the Product Law repeatedly with g(x) = f(x) gives the following Power Law: Here are two obvious but useful limits: Here are two obvious but useful limits:

13. Further Properties (cont’d)

14. more examples

16. To review: A 2 nd algebraic technique is multiplying by a conjugate To review: A 2 nd algebraic technique is multiplying by a conjugate

17.  Think of the number of teachers hired with respect to students enrolled.

19. Review Using the Limit Laws to calculate limits Using the Limit Laws to calculate limits Additional Properties of Limits Additional Properties of Limits Direct Substitution Property Direct Substitution Property

20. Assignment 7 p. 115 1-23 odd, 37 p. 115 1-23 odd, 37