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

(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 o -1^-} F(x) = ) 2. (lim_{x o -1^+} F(x) = ) 3. (lim_{x o -1} F(x) = ) 4. (F(-1) = ) 5. (lim_{x o 1^-} F(x) = ) 6. (lim_{x o 1^+} F(x) = ) 7. (lim_{x o 1} F(x) = ) 8. (lim_{x o 3} F(x) = ) 9. (F(3) = ) The graph of (y = F(x)).

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00:01 Here, we're given the graph of a function, and we're asked to compute some details, mostly limits.

00:06 So for the first question here, we're asked for the limit as x approaches negative 1 from the left.

00:12 So to do a one -sided limit, we're just going to find the x value that's here of negative 1.

00:17 And we go to the left.

00:18 You find your graph, and then go infinitely close to x equals negative 1 by following the graph.

00:25 So as i get infinitely close, i get to 0.

00:29 Notice i can never actually reach zero, but i can get infinitely close to it, and that's what a limit is.

00:35 Now, if i go for number two, that's the limit from the right.

00:41 Well, i'm going to do the same thing, go to negative one, go to the right, find my graph, and then follow until i get infinitely close to zero, or to negative one, and again, i'm going to get to zero.

00:52 And what that means is for number three, the overall limit, there's no left or right.

00:57 Well, that's going to be zero.

00:59 The only way the limit can exist if both left and right are the same.

01:03 And in this case, they are.

01:04 They're both zero.

01:07 So now if i look at number four, that says what is f of negative 1? that says, don't worry about what happens around the function.

01:14 I only care about exactly at negative 1...

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