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Welcome to Calculus

Welcome to Calculus. Get out your ASGN. Warm up . POP QUIZ!. Using f & g, graphically find the limits for # 1-6. f(x). Pop Quiz. g(x). Algebraically, find the limit of each in #7-10. Pop Quiz. Answers. 2 1 DNE 4 0 DNE. 3/2 1/3 3 1.

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Welcome to Calculus

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  1. Welcome to Calculus Get out your ASGN

  2. Warm up

  3. POP QUIZ!

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

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

  6. Answers • 2 • 1 • DNE • 4 • 0 • DNE 3/2 1/3 3 1

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

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

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

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

  11. 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: • Here are two obvious but useful limits:

  12. Further Properties (cont’d)

  13. more examples

  14. When factoring does not work

  15. More examples To review: A 2nd algebraic technique is multiplying by a conjugate

  16. Think of the number of teachers hired with respect to students enrolled. Greatest Integer Function

  17. Examples

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

  19. Assignment 7 • p. 115 1-23 odd, 37

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