Two multiple choice questions?

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. 

The graph of the function below might help

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

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

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

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

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?

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.

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.

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?