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ChrisV

  • 2 years ago

lim x>4- ([[x]]-7)

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  1. ChrisV
    • 2 years ago
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    \[\lim_{x \rightarrow 4-} ([[x]] -7)\]

  2. rickjbr
    • 2 years ago
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    greatest integer function, it will be a horizontal line from (3<=x<4)

  3. ChrisV
    • 2 years ago
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    yea i have seen graphs of these functions

  4. ChrisV
    • 2 years ago
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    looks sorta like steps

  5. rickjbr
    • 2 years ago
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    yes

  6. ChrisV
    • 2 years ago
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    but i have no idea how to graph one myself

  7. ChrisV
    • 2 years ago
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    i am assuming if I graphed this I could see the limit

  8. ChrisV
    • 2 years ago
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    which according to the book is 8

  9. rickjbr
    • 2 years ago
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    You're approaching x=4 from the left, correct?

  10. ChrisV
    • 2 years ago
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    they need a grapher on this site

  11. ChrisV
    • 2 years ago
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    yes from the left

  12. rickjbr
    • 2 years ago
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    If you're approaching 4 from the left, [[x]] will be 3

  13. ChrisV
    • 2 years ago
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    so how to i determine the points i need to plot on [[x]]-7

  14. ChrisV
    • 2 years ago
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    you have to take into account the -7

  15. rickjbr
    • 2 years ago
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    yes, so -4 overall

  16. rickjbr
    • 2 years ago
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    It's just the graph of f(x)=[[x]] shifted down 7 units

  17. ChrisV
    • 2 years ago
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    well the book says 8 so .... >.<

  18. ChrisV
    • 2 years ago
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    oh i know why

  19. ChrisV
    • 2 years ago
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    i missed a 5 lol

  20. ChrisV
    • 2 years ago
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    5[[x]]-7

  21. ChrisV
    • 2 years ago
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    so to graph this

  22. rickjbr
    • 2 years ago
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    yes, so 5(3)-7=8

  23. rickjbr
    • 2 years ago
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    If you were approaching from the right, [[x]] would be 4

  24. ChrisV
    • 2 years ago
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    yes i understnad that

  25. rickjbr
    • 2 years ago
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    so you don't know how to graph the greatest integer function?

  26. ChrisV
    • 2 years ago
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    nope i dont

  27. ChrisV
    • 2 years ago
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    i know what they look like

  28. ChrisV
    • 2 years ago
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    but not how to graph one given an equation

  29. rickjbr
    • 2 years ago
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    |dw:1329178784965:dw|

  30. rickjbr
    • 2 years ago
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    that is f(x)=[[x]]

  31. rickjbr
    • 2 years ago
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    for 0-3

  32. ChrisV
    • 2 years ago
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    yea how do i know to start at 0 and stop 1

  33. ChrisV
    • 2 years ago
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    then start at 1,2 and stop at 2,1

  34. ChrisV
    • 2 years ago
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    oops 1,1

  35. rickjbr
    • 2 years ago
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    greatest integer function definition, [[x]] is the greatest integer less than or equal to x

  36. rickjbr
    • 2 years ago
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    f(x)=[[x]] f(3.999999999999999999999)=3 f(3)=3 f(4)=4

  37. ChrisV
    • 2 years ago
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    so by definition if x=1 then [[x]] is x>= 1

  38. ChrisV
    • 2 years ago
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    i mean <=1

  39. rickjbr
    • 2 years ago
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    if x=1, [[x]]=1

  40. rickjbr
    • 2 years ago
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    Just think of it as going down the steps instead of up...you'll start as close as you can to [[x]]+1 and end up at [[x]]

  41. rickjbr
    • 2 years ago
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    but you're not actually starting at [[x]] + 1

  42. rickjbr
    • 2 years ago
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    so an open circle

  43. rickjbr
    • 2 years ago
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    it is defined at all integers, but not continuous at any integer

  44. ChrisV
    • 2 years ago
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    so if I were doing 5[[4]]-7 i would plot from (4,13) t0 (5,13) with an open point at (5,13)?

  45. rickjbr
    • 2 years ago
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    yes, open circle at (5,13), closed at (4,13)

  46. ChrisV
    • 2 years ago
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    and if it happened to be [[-x]] i would just reflect

  47. rickjbr
    • 2 years ago
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    across the y axis, yes

  48. ChrisV
    • 2 years ago
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    thanks

  49. rickjbr
    • 2 years ago
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    np

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