- 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?

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- 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.

##### 1 Attachment

- ganeshie8

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

- ganeshie8

for example
[3.5] = 3

Looking for something else?

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

## More answers

- ganeshie8

see if you can find [2.88]

- 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

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

- ganeshie8

Yes, can you answer my earlier question

- elleblythe

- ganeshie8

how about [-5.33] ?

- elleblythe

@ganeshie8 -6

- ganeshie8

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

- ganeshie8

|dw:1435246737205:dw|

- ganeshie8

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

- ganeshie8

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

- elleblythe

@ganeshie8 1 and 2

- ganeshie8

thats it!

- elleblythe

@ganeshie8 So how about the (-)??

- ganeshie8

|dw:1435247060087:dw|

- 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

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

- 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

|dw:1435247787651:dw|

- elleblythe

|dw:1435248013287:dw|

- elleblythe

- ganeshie8

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

- 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

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

- ganeshie8

yw!

Looking for something else?

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