1. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 1

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3. 3 A limit gives us language for describing how function values (y-values) behave as the domain values (x-values) approach some particular number (or ∞ or -∞). In other words, a limit tells us: what the y-values of a function are approaching as x approaches some value c (but not necessarily equal to c) or it tells us the intended y-value of a function as x approaches c (we will see this when x approaches a hole).

4. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 4 The limit as x approaches a number whose function value is definite:

5. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 5 The limit as x approaches an asymptote: (limits that fail to exist)

6. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 6 Another example of when a limit fails to exist : : Parent signature and test corrections on loose-leaf!!!

7. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 7 The limit as x approaches a hole:

8. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 8 Some more examples:

9. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 9

10. 10 SUMMARY OF THE RELATIONSHIP BETWEEN HORIZONTAL AND VERTICAL ASYMPTOTES AND LIMITS: HORIZONTAL ASYMPTOTE VERTICAL ASYMPTOTE

11. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 11 END-BEHAVIOR MODEL (EBM) FOR RATIONAL FUNCTIONS: HOW DO WE USE THIS END-BEHAVIOR MODEL (EBM): EXAMPLE OF (EBM):

12. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 12 WHEN HAVE WE USED THE “EBM” IN A SIMILAR FASHION? To find horizontal asymptotes. LET’S EXAMINE THE PREVIOUS EXAMPLE MORE CLOSELY:

13. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 13

14. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 14

15. AIM: WHAT IS A LIMIT? HW#59 p. 218 – 219 # 14, 17, 18, 19, 20 p. 219 # 26 27, 29a 15 Review for Test: