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+3
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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

 

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

 Sep 20, 2014

Best Answer 

 #7
avatar+30354 
+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. 

 Sep 21, 2014
 #1
avatar+30354 
+8

The graph of the function below might help

f(x)

 Sep 20, 2014
 #2
avatar+109736 
+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?

 Sep 20, 2014
 #3
avatar+30354 
+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

 Sep 20, 2014
 #4
avatar+109736 
+3

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

 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?

 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

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

 Sep 20, 2014
 #7
avatar+30354 
+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+109736 
+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.

 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?

 Sep 21, 2014

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