elleblythe
  • elleblythe
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?
Mathematics
chestercat
  • chestercat
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elleblythe
  • elleblythe
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.
ganeshie8
  • ganeshie8
[x] is the greatest "integer" less than or equal to x
ganeshie8
  • ganeshie8
for example [3.5] = 3

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ganeshie8
  • ganeshie8
see if you can find [2.88]
elleblythe
  • elleblythe
@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 (-)?
elleblythe
  • elleblythe
@ganeshie8 Take a loot at the screenshot I posted for a clearer picture of what I'm trying to say.
ganeshie8
  • ganeshie8
Yes, can you answer my earlier question
elleblythe
  • elleblythe
ganeshie8
  • ganeshie8
how about [-5.33] ?
elleblythe
  • elleblythe
ganeshie8
  • ganeshie8
great! just making sure :) lets get to the question in attachment
ganeshie8
  • ganeshie8
|dw:1435246737205:dw|
ganeshie8
  • ganeshie8
\(x\to 1^{+}\) means you're approaching \(1\) from the right hand side, so let \(x=1.001\) maybe
ganeshie8
  • ganeshie8
[1.001] = ? [4-1.001] = ?
elleblythe
  • elleblythe
@ganeshie8 1 and 2
ganeshie8
  • ganeshie8
thats it!
elleblythe
  • elleblythe
@ganeshie8 So how about the (-)??
ganeshie8
  • ganeshie8
|dw:1435247060087:dw|
elleblythe
  • elleblythe
@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?
elleblythe
  • elleblythe
@ganeshie8 And how did she come up with 3 and 2 in defining [[4-x]]?
ganeshie8
  • ganeshie8
\[4-n\ge x\gt 3-n\] 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
ganeshie8
  • ganeshie8
|dw:1435247787651:dw|
elleblythe
  • elleblythe
|dw:1435248013287:dw|
elleblythe
  • elleblythe
ganeshie8
  • ganeshie8
when you substitute \(x=1^{+}\) into \(4-x\), you do get something less than \(3\), which is expressed mathematically as \(3^{-}\), yes ?
ganeshie8
  • ganeshie8
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)
elleblythe
  • elleblythe
@ganeshie8 Okay I understand now, thank you very much!
ganeshie8
  • ganeshie8
yw!

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