00:01
So just as a bit of a purpose, we're going to look at this graph here that i have just kind of thrown together on the fly.
00:11
And we'll call this 3, 2, and 1.
00:20
So if this is the graph that we were to start with, there are several things that we need to know.
00:27
If we were trying to find the limit as x approaches a from the left, that would be this.
00:34
Right here coming up on it from from the side that's less than it the negative side from the left it looks like it's approaching two but the limit as x approaches a from the right coming at it from this direction it looks like it's approaching one so because of that the limit as x approaches a does not exist even though we have this point up here at three where our function is defined because the limit as x approaches from the left and the limit as x approaches from the right are not the same the limit at a does not exist now at b here the the the limit as x approaches b is actually going to be equal to the value of the function at b which in this case is just going to be about to so it's actually defined right there and so that is really helpful.
01:39
In a case like c, the limit as x approaches c from either direction, so from the left or from the right, is going to equal 3, which means the limit as x approaches c also equals 3, but the value of the function is actually closer to 1.
02:02
So that's just some of the basics that are going to guide this question.
02:10
So there are a bunch of values, that we want to find starting out with a, the value of the function at 1, which is going to be like this, our example c right here.
02:26
So the value of the function is going to be 3 in this case.
02:31
So f of 1 equals 3...