Question

Use the graph below to answer the following question: List the integer value(s) of x in the open interval from –2 to 5 where the limit exists as a finite value as x approaches those integer value(s).

Answer 1

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}