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DiffCalculus: September 12, 2012

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DiffCalculus: September 12, 2012

  1. 1. 1. LimitsFor you, what is a limit?
  2. 2. 1. Limits
  3. 3. 1. Limits
  4. 4. 1. Limits
  5. 5. 1. Limits
  6. 6. 1. LimitsLet’s work it out for x = 1
  7. 7. 1. LimitsLet’s work it out for x = 1
  8. 8. 1. Limits
  9. 9. 1. Limits The limit of (x2 - 1)/(x - 1) as x approaches 1 is 2
  10. 10. 1. Limits The limit of (x2 - 1)/(x - 1) as x approaches 1 is 2
  11. 11. 1. Limits
  12. 12. 1. Limits"ignoring what happens when you get there, but asyou get closer and closer the answer gets closer andcloser to 2"
  13. 13. 1. Limits"ignoring what happens when you get there, but asyou get closer and closer the answer gets closer andcloser to 2"
  14. 14. 1. LimitsCommon Sense DefinitionA limit is the intended height of a function.
  15. 15. 1. LimitsWhen it is different from different sides.
  16. 16. 1. LimitsWhen it is different from different sides.
  17. 17. 1. LimitsWhen it is different from different sides.
  18. 18. 1. LimitsWhen it is different from different sides.
  19. 19. 2. ExamplesFind the following limits:
  20. 20. 2. ExamplesFind the following limits: =1
  21. 21. 2. ExamplesFind the following limits: =1 =DNE
  22. 22. 2. ExamplesFind the following limits: =1 =DNE =2
  23. 23. 2. ExamplesFind the following limits: =1 =DNE =2 = −∞
  24. 24. 2. ExamplesTrue or False: ! DNE ! DNE ! DNE
  25. 25. 2. ExamplesTrue or False: ! False DNE ! DNE ! DNE
  26. 26. 2. ExamplesTrue or False: ! False DNE False ! DNE ! DNE
  27. 27. 2. ExamplesTrue or False: ! False DNE False ! False DNE ! DNE
  28. 28. 2. ExamplesTrue or False: ! False DNE False ! False DNE True ! DNE
  29. 29. 2. ExamplesTrue or False: ! False DNE False ! False DNE True ! True DNE
  30. 30. 2. ExamplesTrue or False: ! False DNE False ! False DNE True ! True DNE False

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