11X1 T08 01 limits & continuity

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  • 1. Limits & Continuity

2. Limits & Continuity A limit describes the behaviour of functions. 3. Limits & Continuity A limit describes the behaviour of functions. 4. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach? 5. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach? 6. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach? 7. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 y x 8. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 y x 9. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 y x y x 10. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 y x y x 11. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 y x y x 12. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 as thexvalue approachesafrom the positive side ,what value doesf ( x ) approach?y x y x 13. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 as thexvalue approachesafrom the positive side ,what value doesf ( x ) approach?y x y x 14. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 as thexvalue approachesafrom the positive side ,what value doesf ( x ) approach?y x y x 15. Limits & Continuity A limit describes the behaviour of functions. as thexvalue approachesa ,what value doesf ( x ) approach?as thexvalue approachesafrom the negative side ,what value doesf ( x ) approach?1 1 4 6 as thexvalue approachesafrom the positive side ,what value doesf ( x ) approach?y x y x 16. Finding Limits 17. Finding Limits (1) Direct Substitution 18. Finding Limits (1) Direct Substitution 19. Finding Limits (1) Direct Substitution 20. Finding Limits (1) Direct Substitution (2) Factorise and Cancel 21. Finding Limits (1) Direct Substitution (2) Factorise and Cancel 22. Finding Limits (1) Direct Substitution (2) Factorise and Cancel 23. Finding Limits (1) Direct Substitution (2) Factorise and Cancel 24. Finding Limits (1) Direct Substitution (2) Factorise and Cancel 25. (3) Special Limit 26. (3) Special Limit 27. (3) Special Limit 28. (3) Special Limit 29. (3) Special Limit 30. (3) Special Limit 31. (3) Special Limit 32. (3) Special Limit 33. (3) Special Limit 34. (3) Special Limit 35. 36. 37. 38. 39. 40. 41. 42. Exercise 7I; 1a, 2ace, 3ac, 4a, 5ad, 8a, 9ab, 10a