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1. PAGE 917 14.1: Introduction to Limits

2. PROPERTIES OF LIMITS SECTION 14.2

3. DIFFERENT FORMS OF LIMITS • Always plug in the number to confirm the form of limit • It will fit into these forms of limits: 1. Easy Limits: Plug in x to f(x) to get the limit 2. “0/0” Limits • Plug in x to prove 0/0 • Apply Algebra Factoring Rules • Plug in x to f(x) to get the limit REMEMBER: IT IS WHAT X APPROACHES NOT WHAT X IS 14.1: Introduction to Limits

4. EXAMPLE 1 Evaluate 14.1: Introduction to Limits

5. EXAMPLE 2 Evaluate 14.1: Introduction to Limits

6. EXAMPLE 3 Evaluate 14.1: Introduction to Limits

7. EXAMPLE 4 Evaluate 14.1: Introduction to Limits

8. YOUR TURN Evaluate 14.1: Introduction to Limits

9. EXAMPLE 5 Use given below, determine 14.1: Introduction to Limits

10. EXAMPLE 6 Use given below, determine 14.1: Introduction to Limits

11. YOUR TURN Use given below, determine 14.1: Introduction to Limits

12. EXAMPLE 7 Evaluate What form is this? AS X APPROACHES 4, F(X) OR Y APPROACHES 8. 14.1: Introduction to Limits

13. EXAMPLE 7 Evaluate 14.1: Introduction to Limits

14. EXAMPLE 8 Evaluate 14.1: Introduction to Limits

15. YOUR TURN Evaluate 14.1: Introduction to Limits

16. EXAMPLE 9 Evaluate What form is this? NO NEED TO FOIL THE BOTTOM 14.1: Introduction to Limits

17. EXAMPLE 9 Evaluate 14.1: Introduction to Limits

18. EXAMPLE 10 Evaluate 14.1: Introduction to Limits

19. YOUR TURN Evaluate 14.1: Introduction to Limits

20. DIFFERENCE QUOTIENT • The Limit of a Difference Quotient is used to find the slope of the curves • It is also the slope of the tangent line 14.1: Introduction to Limits

21. EXAMPLE 11 Given f(x) = 2x2, find the slope at x = –3 14.1: Introduction to Limits

22. EXAMPLE 11 Given f(x) = 2x2, find the slope at x = –3 14.1: Introduction to Limits

23. EXAMPLE 12 Given f(x) = x2, find the slope at x = 5 14.1: Introduction to Limits

24. YOUR TURN Given f(x) = x2 – 1, find the slope at x = 3 14.1: Introduction to Limits

25. ASSIGNMENT Worksheet 14.1: Introduction to Limits