A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

elleblythe

  • one year ago

Greatest Integer Function: In defining [[1-3x]], As x->0+, 1-3x->1*-, [[1-]]=0, why is the sign of the 1* negative? How will we know if it is negative or positive?

  • This Question is Closed
  1. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Also, in defining [[4-x]], how did we come up with 3 and 2? I'm not asking for the solution, just the definition. No solving is needed for these questions.

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    [x] is the greatest "integer" less than or equal to x

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for example [3.5] = 3

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    see if you can find [2.88]

  5. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 Yeah I understand how to find the greatest integer function but my professor requires us to define the greatest integer function, and I'm just wondering how to know the sign of 1*? Why is it (-)?

  6. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 Take a loot at the screenshot I posted for a clearer picture of what I'm trying to say.

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, can you answer my earlier question

  8. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 2

  9. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how about [-5.33] ?

  10. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 -6

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    great! just making sure :) lets get to the question in attachment

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435246737205:dw|

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(x\to 1^{+}\) means you're approaching \(1\) from the right hand side, so let \(x=1.001\) maybe

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    [1.001] = ? [4-1.001] = ?

  15. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 1 and 2

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats it!

  17. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 So how about the (-)??

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435247060087:dw|

  19. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 Sadly, I can't skip it because my teacher requires us to write it down in our exams. How do we know if the value inside the [[]] is coming from the right or left?

  20. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 And how did she come up with 3 and 2 in defining [[4-x]]?

  21. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[4-n\ge x\gt 3-n\] it was just a guess, you plugin \(n=3\) : \[4-3\ge x\gt 3-3\\~\\1\ge x\gt 0\] which is not what we want so discard this and plugin \(n=2\) in next trial

  22. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435247787651:dw|

  23. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435248013287:dw|

  24. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8

  25. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when you substitute \(x=1^{+}\) into \(4-x\), you do get something less than \(3\), which is expressed mathematically as \(3^{-}\), yes ?

  26. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here is how we interpret -,+ in the top of a number : \(3^{+}\) : right of \(3\) (example : 3.001) \(3^{-}\) : left of \(3\) (example : 2.999)

  27. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 Okay I understand now, thank you very much!

  28. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw!

  29. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.