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lucy4104 Group Title

is lim as x approaches c the same as f(c)?

  • one year ago
  • one year ago

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  1. ghazi Group Title
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    where is the function f(c)

    • one year ago
  2. lucy4104 Group Title
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    c=3, f(x)= (x^2+5)/(x-6) continuous or no?... is the question.

    • one year ago
  3. ByteMe Group Title
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    at c=3, yes... the function is defined at x=3 so the limit of f is f(3)

    • one year ago
  4. lucy4104 Group Title
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    what if x=c is not defined?

    • one year ago
  5. ByteMe Group Title
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    if f(x) is not defined at x=c, then the limit can still exist but not necessarily at f(c). also, if there is a vertical asymptote at x=c, then the limit does not exist.

    • one year ago
  6. lucy4104 Group Title
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    the limit can still exist but not necessarily at f(c)?

    • one year ago
  7. ByteMe Group Title
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    yes... for example... |dw:1361168628388:dw| here, the limit of f(x) as x approaches c is a.... NOT f(c)

    • one year ago
  8. lucy4104 Group Title
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    OHHH so then in that case it would be dicontinuous? When can you tell, or what can you do, to know that something is continuous, but algebraically? step by step and explain?

    • one year ago
  9. ByteMe Group Title
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    yes... but in your original function, it is continuous at all x values except at x=6. so in your problem, the limit of f as x approaches c for any value OTHER THAN 6, will be f(c)

    • one year ago
  10. lucy4104 Group Title
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    oh! so then if x=6 was not an asymptote, but a hole, the limit would be equivalent to f(c)??

    • one year ago
  11. ByteMe Group Title
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    ***IF*** the function was CONTINUOUS at x=6, then the limit would be f(6)

    • one year ago
  12. ByteMe Group Title
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    seems like we're going in circles here but we're not... Continuity of a funtion is defined in terms of limits....

    • one year ago
  13. lucy4104 Group Title
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    so...no?

    • one year ago
  14. ByteMe Group Title
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    if the "hole" you're referring to is a REMOVABLE discontinuity, then yes, the limit would be f(6) or as you said, f(c)...

    • one year ago
  15. lucy4104 Group Title
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    yes!!!! ok, thank you!

    • one year ago
  16. ByteMe Group Title
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    yw...:)

    • one year ago
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