+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
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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.
+33661 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.
+118687 I'm sorry I have not seen questions like these before.
I do not know the notation [[x]] It is a mystery to me?
+33661 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
+118687 Have you seen notation like this before or is it just an educated guess?
+564 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?
+564 I finally found it in my textbook, but there is only one example. 
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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.
+33661 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.
+118687 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.
+564 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?
