1. Warm-Up Thoughts(after 1.2) Why do piece-wise functions and rational functions make for great “limit” examples and discussion. Think of at least 3 reasons and be ready to share out. If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2? Explain your reasoning. If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain your reasoning.

2. How was HW #1-26 Section 1.2 Did you check your ODD answers in the back of the book? I have EVEN answers on the back whiteboard. Most of the time, I will post the scanned answer key online on my website since it shows step-by-step but I wait until after our first day of discussion to do this. I want to hear from you! What went wrong? Why?

3. Syllabus Let’s talk through this today.

4. Reflection on Reading of 1.2

5. SECTION 1.3 EVALUATING LIMITS ANALYTICALLY

6. Question for You…

7. Are You Behaving For Me? Since most of our functions are “well behaved” and continuous (watch out for discontinuous functions), a limit can be found by direct substitution. Why?Why?Why?

8. Theorem 1.1 Some Basic Limits

9. Theorem 1.2 Properties of Limits See page 59 of the text Let us talk through each of these carefully and think about why they are true statements.

10. The Limit of a Polynomial

11. Limit of a Rational Function Can direct substitution be a quick approach to finding a limit of a rational? Why or why not? With rationals, what do you always need to be watchful of? (Do this 2 ways: 1 st with the properties of limits and the 2 nd with direct substitution)

12. The Limit of a Radical Function Can direct substitution be a quick approach to finding a limit of a radical function? Consider an even root versus and odd root. Why or why not?

13. The Limit of a Composite Function

14. Limits of Trig Functions When would direct substitution fail?

15. Practice: Think about what property you are applying.

16. What’s This?

17. Indeterminate Form Continued

18. Two Special Trig Limits You must memorize these!!!

19. Challenge (if time permits)

20. Closure: Strategy for Finding Limits Learn to recognize which limits will allow direct substitution. Apply the properties such as composite, radical, rational, sum and difference, scalar, quotient, etc. Use a graph Use a table via the calculator Algebraic techniques (simplify the fraction, rationalize the numerator, use a conjugate as a fancy 1, use a trig. identity…just get creative)

21. Homework Section 1.3 #1-81 multiples of 3 (since we will have another worksheet to review indeterminate form) Remember: Your job is to isolate the problems you can’t do and ask me in class the next day! READ Section 1.3 if you need more clarification. We will cover the Squeeze Theorem a little bit later.