$\newcommand{\[}{[\![}\newcommand{\]}{]\!]}$So, I'm again reading a calculus book which presents a problem (below) that's not explained in the chapter. Or maybe it does, but it's poor use of language is throwing me off. The professor only being available 2/7 days of the week is starting to become a hindrance.
I understand Greatest Integer Function (the "stair steps" as my teachers had called it). I've got the graph of $y=\[x\]$. I don't even understand what is being asked, with the "calculate for $c$ an integer". I think it is wanting me to deduce some sort of generic rule for it?
I don't want this textbook question solved as I want to know what it's asking for.
The greatest integer function, also known as the floor function, is defined by $\[x\] = n$, where $n$ is the unique integer such that $n ≤ x < n + 1$. Sketch the graph of $y = \[x\]$. Calculate for $c$ an integer:
- $\lim_{x→c−} \[x\]$
- $\lim_{x→c+} \[x\]$
- $\lim_{x→2.6}\[x\]$
It means "Suppose $c$ is an integer, then calculate:"
Now you need to find the left and right limit of $\[x\]$ at this integer $c$. Draw the graph and you see exactly what these limits are.