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anonymous

  • 4 years ago

f(x)=[[x]] what does the double bracket mean?

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  1. anonymous
    • 4 years ago
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    It means any x will be the integer below it, for example f(1.999)=1

  2. anonymous
    • 4 years ago
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    f(-3.2222)=-4

  3. anonymous
    • 4 years ago
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    but they want me to get the derivative of it and graph the derivative..

  4. anonymous
    • 4 years ago
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    and they get a really weird graph, where it is unknown on every whole number

  5. anonymous
    • 4 years ago
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    |dw:1328116598663:dw|The graph of f(x)=[[x]] looks like

  6. anonymous
    • 4 years ago
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    yes, but they want me to get the derivative, one second let me draw it

  7. anonymous
    • 4 years ago
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    It's called the "greatest integer function"

  8. anonymous
    • 4 years ago
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    It's not differentialiable at any integers because the graph is discontinuous at all integers

  9. anonymous
    • 4 years ago
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    |dw:1328116744272:dw|

  10. anonymous
    • 4 years ago
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    that is a bar drawing, but ya get the picture

  11. anonymous
    • 4 years ago
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    Any the derivative everywhere else is 0

  12. anonymous
    • 4 years ago
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    because they are horizontal lines

  13. anonymous
    • 4 years ago
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    so.. the double brackets means that it is discontinuous at all integers?

  14. anonymous
    • 4 years ago
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    no...the double brackets mean it's the greatest integer function

  15. anonymous
    • 4 years ago
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    as you can see from my crude drawing, at every integer the graph is discontinous

  16. anonymous
    • 4 years ago
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    they if it is "greatest integer" wouldn't ti still be an integer?

  17. anonymous
    • 4 years ago
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    The greatest integer function means the greatest integer less than x

  18. anonymous
    • 4 years ago
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    less than or equal to x

  19. anonymous
    • 4 years ago
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    but x is a variable

  20. anonymous
    • 4 years ago
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    yes...

  21. anonymous
    • 4 years ago
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    But if you plug in any value for x, say 1.98271, f(x)=1

  22. anonymous
    • 4 years ago
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    then if it = 1 then why is it not defined at one? and i am sorry I am not understanding this

  23. anonymous
    • 4 years ago
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    The differential is not defined at 1, f(x)=[[x]] is defined

  24. anonymous
    • 4 years ago
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    oh, now i get it, because we are getting the derative of it that is why it is 0

  25. anonymous
    • 4 years ago
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    sorry, my mind just wasn't working on all 4 cylinders

  26. anonymous
    • 4 years ago
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    i get it now

  27. anonymous
    • 4 years ago
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    lol no problem

  28. anonymous
    • 4 years ago
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    thx for your time

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