limx to 2 fx limx to 2 fx limx to 2 fx limx to 3 fx limx to 3 fx limx to 3 fx 82153

Name: limx to 2 fx limx to 2 fx limx to 2 fx limx to 3 fx limx to 3 fx limx to 3 fx 82153
Uploaded: 2019-07-03T19:52:22-08:00
Duration: 3 min 36 s
Channel: Paul George
Description: limx to 2 fx limx to 2 fx limx to 2 fx limx to 3 fx limx to 3 fx limx to 3 fx 82153

Step 1: As $x$ approaches 2 from the left, the function approaches 3.

Limx to 2 fx limx to 2 fx limx to 2 fx limx to 3 fx limx to...

Transcript

00:01 Hey everybody.

00:02 We're doing chapter two, section three, problem 12.

00:05 This problem is really interesting because it deals with actually the other way around, where in terms of some problems, they might give you a graph, and tell you some things about it, it gives you information, and wants you to make a graph.

00:16 And i think it's important to be able to do both directions.

00:18 So this problem has six different characteristics to it.

00:22 And that might seem kind of overwhelming at first.

00:24 I'm here to try to make it seem less confusing.

00:27 So first off, if we're making a graph, i like to make a cartesian plane.

00:30 So we got the x's, we got the y's, and now the question now is, okay, well, what do we do with it? if you look down at the points, try to look at where the limits are, like the x values, right? you have something approaching zero, you have something approaching four, and that's it.

00:48 So if i'm looking at that, that i know that i want to talk about zero and i also want to talk about four.

00:55 I, in terms of this, i don't actually care about what's happening to the left of zero or to the right of zero.

01:02 I just know the important stuff is going to come from the left and right of zero and at zero and the left and right of four and at four.

01:08 And that's what i care about.

01:09 So now in terms of how to scale, you know, maybe the vertical part, the y.

01:14 If i look at the limit, i see that there's a two, there's a zero, there's a three, there's a zero, there's a two and a one.

01:22 I never see it going above four.

01:25 So for me, i'm just going to draw one, two, three, and four, and then one, two, three, and four, and then one, three, and four.

01:32 That seems to capture all that we need for right now.

01:35 So if we go one at a time, right, the limit as x approach to zero from the left is two.

01:41 So if i walk from the left side, right, come from the left, i know that i'm going to land at two.

01:48 And i'm drawing an empty circle on purpose.

01:50 It's a limit.

01:51 I don't actually know if that point exists at zero.

01:55 That is not information i am privy to yet.

01:57 I'm coming from the left, right? i don't exactly know what happens as we go out, but that's okay.

02:03 If i'm coming from the left, right, i end up at zero.

02:06 Then the next part says if i come from the right, i end up actually at zero instead of at two.

02:11 So that's interesting...

Question

$\lim_{x \to 2^-} f(x) = $ $\lim_{x \to 2^+} f(x) = $ $\lim_{x \to 2} f(x) = $ $\lim_{x \to 3^-} f(x) = $ $\lim_{x \to 3^+} f(x) = $ $\lim_{x \to 3} f(x) = $

Question

$\lim_{x \to 2^-} f(x) = $ $\lim_{x \to 2^+} f(x) = $ $\lim_{x \to 2} f(x) = $ $\lim_{x \to 3^-} f(x) = $ $\lim_{x \to 3^+} f(x) = $ $\lim_{x \to 3} f(x) = $

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