If these permutations were in a line, then the equation would be n!. But since we are dealing with a circle, it's a little bit different, given that there is no specific beginning or end. This means that <span>you could rotate the circle around n different ways and still have the same circular permutation. Thus, this would be the expression you are looking for:
n!/n, which can be simplified as (n-1)!
The correct answer is the second option.</span>
To start off, the wording of this question is pretty technical. Let's reword the question to make it a bit easier to understand.
From the open interval from -2 to 5 (meaning between but not including those integers), list every integer for x at which x approaches a defined y point on the curve, regardless of whether it actually takes that y value at that point.
Let's start with the first eligible integer, -1.
The limit, from both sides, as x approaches -1 is y=-1.
However, y = -2 at this point.
At 0, x continuous and defined on the curve where you would expect it, and therefore the limit at x=0 is its y value at that point, 0.
x=1 is not eligible, because its left-side limit (when approaching from the left) and right-side limit (when approaching from the right), are distinct.
x=2 has a clear defined limit. It is continuous and defined at that point. The limit looks to be around y= 1.8
x=3 does not feature a clearly defined, finite value, since the limit at x=3 is
-∞
x=4, like x=0 and x=2, has a clear and finite limit, since it is continuous at that point.
Answers are x=-1, x=0, x=2, and x=4
or
{-1, 0, 2, 4}
