+0  
 
+3
387
9
avatar+564 

The greatest integer, function, represented by $$f(x)=[[x]]$$ is continuous:

a. everywhere, all real numbers

b. on its domain

c. only where x is an integer

d. none of these

 

------------------

Determine the value of $$\lim_{x\rightarrow1} [ [x] ]$$

 

a. 0

b. DNE

C. 1

D. None of these

 

-------------------------------------------

I'm going to try and look inside my textbook as well. 

chilledz3non  Sep 20, 2014

Best Answer 

 #7
avatar+26745 
+10

Ok.  It's the largest integer less than or equal to x, whereas I assumed it was the smallest integer greater than or equal to x.  The graph will look pretty much the same though, except it will be shifted along the x-axis by one unit!

 

And your limit calculations are correct chilledz3non. 

Alan  Sep 21, 2014
 #1
avatar+26745 
+8

The graph of the function below might help

f(x)

Alan  Sep 20, 2014
 #2
avatar+92775 
+8

I'm sorry I have not seen questions like these before.

I do not know the notation [[x]]       It is a mystery to me?

Melody  Sep 20, 2014
 #3
avatar+26745 
+8

I've taken this notation to mean the nearest integer that is greater than or equal to x.

e.g. if x = 2.1 then [[x]] = 3

if x = 1 then [[x]] = 1 

if x = -1.5 then [[x]] = -1

Alan  Sep 20, 2014
 #4
avatar+92775 
+3

Have you seen notation like this before or is it just an educated guess?

Melody  Sep 20, 2014
 #5
avatar+564 
+3

So judging from your graph Allen, I'm going to say that $$f(x)=[[x]]$$ is not continuous anywhere, since you have to lift your pencil to draw the graph. Am I right or wrong?

chilledz3non  Sep 20, 2014
 #6
avatar+564 
+8

I finally found it in my textbook, but there is only one example. This is the only example in the textbook

-------------------------------------------

I also did some work to prove that the limit does not exist, but I'm not sure if it is correct.

chilledz3non  Sep 20, 2014
 #7
avatar+26745 
+10
Best Answer

Ok.  It's the largest integer less than or equal to x, whereas I assumed it was the smallest integer greater than or equal to x.  The graph will look pretty much the same though, except it will be shifted along the x-axis by one unit!

 

And your limit calculations are correct chilledz3non. 

Alan  Sep 21, 2014
 #8
avatar+92775 
+5

So it is a "Floor" function I think.

 

I think the answer is "none of these"

The function is continuous for every x that is NOT an integer.  That's what I think anyway.

Melody  Sep 21, 2014
 #9
avatar+564 
0

Since I solved the limit and it gave me two different answers for the left side and right side I chose "DNE". Could that be correct as well?

chilledz3non  Sep 21, 2014

12 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.