(1 point) Let F be the function whose graph is shown below....

(1 point) Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a limit does not exist or is undefined, enter "DNE".) 1. lim_{x->-1^-} F(x) = 2. lim_{x->-1^+} F(x) = 3. lim_{x->-1} F(x) = 4. F(-1) = 5. lim_{x->1^-} F(x) = 6. lim_{x->1^+} F(x) = 7. lim_{x->1} F(x) = 8. lim_{x->3} F(x) = 9. F(3) = The graph of y = F(x).

Transcript

00:01 All right, we have a question here about limits, and i've got the function, a reasonable facsimile of the function that you're looking at, and i've also marked the point so that we can just look at those.

00:13 First, we want to know what is the limit of the function as x is approaching negative 1 from the negative side.

00:24 So what that means is that we are looking at the limit of, i don't know, so i want to know.

00:31 What's happening as we're approaching negative 1 from the left -hand side.

00:36 So that means we're approaching it from this direction.

00:40 So as x is approaching negative 1, our function is approaching 2.

00:47 So i know it isn't defined at that point, but the function does not have to be defined in order for the limit to exist.

00:55 So the function at negative 1 is actually defined as 3, but that's not what we're approaching.

01:01 As we're getting closer and closer and closer to negative one, from that left -hand side, we are approaching two.

01:08 And so the limit is two.

01:10 Now similarly, we want to look at the limit as x is approaching negative one from the positive side of our function.

01:19 So that means we're coming in from this side, from that positive side, and we're approaching that same number.

01:26 So this is going to be two again.

01:29 So then it says, well then what is the limit as x is approaching negative 1 of our function? well, since we are approaching, we come in from the left side we're approaching 2.

01:41 We come in from the right side we're approaching 2.

01:44 We are approaching the same number, so the limit exists, and it is 2.

01:51 Now we want to know, what is f of negative 1? well, it turns out that the function at negative 1 is actually defined as 3.

01:59 We've got an open point here at negative 2.

02:04 So that means that we're not actually defined at that point.

02:07 We're defined up here.

02:09 And when the function is, when x is negative 1, the function is 3.

02:15 Now we want to know what is happening...

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