WEBVTT
1
00:00:01.139 --> 00:00:03.109 A:middle L:90%
All right. We've got this limit problem. Um
2
00:00:03.109 --> 00:00:04.759 A:middle L:90%
We want to find this limit or show that it
3
00:00:04.759 --> 00:00:07.120 A:middle L:90%
does not exist. A couple different ways of doing
4
00:00:07.120 --> 00:00:10.449 A:middle L:90%
this. Some people like to do uh low petals
5
00:00:10.449 --> 00:00:13.759 A:middle L:90%
rule because it's fast. Um I don't like that
6
00:00:13.759 --> 00:00:17.440 A:middle L:90%
because limits have to exist before derivatives do. Um
7
00:00:17.440 --> 00:00:19.579 A:middle L:90%
Some people like to think about and behavior that's not
8
00:00:19.579 --> 00:00:22.760 A:middle L:90%
terrible. Um Actually, if X is growing,
9
00:00:23.140 --> 00:00:25.829 A:middle L:90%
I just like to stop it from growing because I
10
00:00:25.839 --> 00:00:28.859 A:middle L:90%
don't know what big really big over really big is
11
00:00:28.859 --> 00:00:30.969 A:middle L:90%
and that's what we have right now. Um So
12
00:00:30.969 --> 00:00:32.350 A:middle L:90%
I'm just gonna make it small. I'm going to
13
00:00:32.350 --> 00:00:37.070 A:middle L:90%
divide top and bottom by X. So three x
14
00:00:37.070 --> 00:00:40.579 A:middle L:90%
divided by X. three. Um And now I
15
00:00:40.579 --> 00:00:44.770 A:middle L:90%
have two times one over X. And then two
16
00:00:44.770 --> 00:00:46.359 A:middle L:90%
X divided by X. Two. And then I
17
00:00:46.359 --> 00:00:49.369 A:middle L:90%
have one times one over X. And then the
18
00:00:49.369 --> 00:00:54.240 A:middle L:90%
only theorem I need for ex growing is as X
19
00:00:54.240 --> 00:00:56.850 A:middle L:90%
gets big one over X gets small. You agree
20
00:00:56.850 --> 00:01:00.289 A:middle L:90%
with that one divided by a really huge Number is
21
00:01:00.289 --> 00:01:03.219 A:middle L:90%
always going to be zero. So then I can
22
00:01:03.219 --> 00:01:07.239 A:middle L:90%
plug that theorem into these limits. Right? Um
23
00:01:07.250 --> 00:01:10.469 A:middle L:90%
limits can add subtract multiply as long as everything exists
24
00:01:10.469 --> 00:01:15.049 A:middle L:90%
. So I have three minus two times zero.
25
00:01:15.060 --> 00:01:15.780 A:middle L:90%
Because that thing is going to be zero. When
26
00:01:15.780 --> 00:01:19.739 A:middle L:90%
X is big divided by two plus zero. So
27
00:01:19.739 --> 00:01:22.879 A:middle L:90%
I'm going to get three minus two times zero divided
28
00:01:22.879 --> 00:01:26.730 A:middle L:90%
by two plus zero is 3/2. I think that's
29
00:01:26.730 --> 00:01:27.159 A:middle L:90%
the cleanest way to think about this