00:01
Okay, so this question gives us a piecewise function, and it asks us to find the limit of x of f of x as x approaches three from the positive direction.
00:19
So basically what this means is if we had a graph, we could just kind of start in the positive direction and follow our line until we get to three, x equals three.
00:31
Since we don't have a graph and we just have a function, we have to think.
00:35
About what this actually means.
00:36
Like what are some x values that are basically greater than three? and we can say that would be things like x equals six, x equals five, x equals four.
00:50
We could start kind of following those closer and closer to three, and that would be approaching three from the positive direction.
00:58
So if we look at our piecewise function, the values that are described in that are described in this kind of last bracket where they tell us negative x squared when x is greater than three um all these values here are greater than three right six is greater than three five is greater than three four is greater than three so if we want to look at approaching three from the positive direction this is the one we're going to look want to look at um for all of our other ones if we're looking between negative six and three that would be approaching x from the negative direction, and likewise for x is less than or equal to negative six.
01:42
All those values are going to get us those are to the left of x, so that would be approaching from the negative direction.
01:48
This last line is the only one that has us approaching from the positive direction so now that we figured that out, all we need to do is substitute three for x and see what we get so let's do that...