WEBVTT
1
00:00:01.340 --> 00:00:04.540 A:middle L:90%
All right, let's answer the question. What is
2
00:00:04.540 --> 00:00:10.259 A:middle L:90%
the behavior off? Why equals two hyperbolic tangent?
3
00:00:10.269 --> 00:00:12.880 A:middle L:90%
Some people call it Van. I like to call
4
00:00:12.880 --> 00:00:14.699 A:middle L:90%
it Tancho, so I'm going to read it that
5
00:00:14.699 --> 00:00:19.949 A:middle L:90%
way. The can't off and sign effects. How
6
00:00:19.949 --> 00:00:22.640 A:middle L:90%
does this thing behave? Okay, let's go ahead
7
00:00:22.640 --> 00:00:25.399 A:middle L:90%
and graphic. If n is equal to one,
8
00:00:25.410 --> 00:00:28.440 A:middle L:90%
you can see that it's kind of going to resemble
9
00:00:28.449 --> 00:00:31.070 A:middle L:90%
a sine function, as you can see right here
10
00:00:31.539 --> 00:00:35.560 A:middle L:90%
. So before we actually observe this, we can
11
00:00:35.810 --> 00:00:42.280 A:middle L:90%
take a look at one Tansi. Looks like if
12
00:00:42.280 --> 00:00:48.000 A:middle L:90%
you recall the tant function resembles that of a inverse
13
00:00:48.000 --> 00:00:51.049 A:middle L:90%
tangent function. Very well. It's just that instead
14
00:00:51.049 --> 00:00:53.939 A:middle L:90%
, off negative power to two pi over to it
15
00:00:53.939 --> 00:00:57.049 A:middle L:90%
actually goes from negative. Want to positive one?
16
00:00:57.060 --> 00:01:00.590 A:middle L:90%
Okay. And if you remember what sign functions looks
17
00:01:00.590 --> 00:01:07.939 A:middle L:90%
like that's actually the end side effects know that it's
18
00:01:07.939 --> 00:01:10.969 A:middle L:90%
simply going to be one of these shapes. And
19
00:01:10.980 --> 00:01:14.280 A:middle L:90%
as an increases or decreases, you can see that
20
00:01:14.280 --> 00:01:18.870 A:middle L:90%
the amplitude changes like that. Mhm. All right
21
00:01:18.879 --> 00:01:21.159 A:middle L:90%
. So as you can imagine, it's going to
22
00:01:21.159 --> 00:01:23.260 A:middle L:90%
be some sort of a mixture of thes to where
23
00:01:23.260 --> 00:01:27.170 A:middle L:90%
you can plug in, uh, Ensign X into
24
00:01:27.180 --> 00:01:32.790 A:middle L:90%
can church and let's see what's gonna happen. Why
25
00:01:32.799 --> 00:01:38.060 A:middle L:90%
equals two engine age off n sign of X.
26
00:01:38.640 --> 00:01:41.840 A:middle L:90%
We already did the one place. Let's see what
27
00:01:41.840 --> 00:01:45.500 A:middle L:90%
happens if it's equal to two. Uh, it
28
00:01:45.500 --> 00:01:48.120 A:middle L:90%
kind of looks a little bit block here, right
29
00:01:48.120 --> 00:01:51.069 A:middle L:90%
? How about a much bigger number? Like 17
30
00:01:51.540 --> 00:01:53.329 A:middle L:90%
? It's getting even Mawr block here. So what's
31
00:01:53.329 --> 00:01:59.829 A:middle L:90%
important to remember about tans? Uh, hyperbolic tangent
32
00:01:59.840 --> 00:02:02.950 A:middle L:90%
is the fact that the upper and the lower bound
33
00:02:02.959 --> 00:02:06.890 A:middle L:90%
of it it's always going to be between negative 1
34
00:02:06.890 --> 00:02:09.159 A:middle L:90%
to 1. So no matter how large the input
35
00:02:09.169 --> 00:02:14.110 A:middle L:90%
is going to be, um, tension is going
36
00:02:14.110 --> 00:02:15.689 A:middle L:90%
to be between negative 1 to 1. However,
37
00:02:15.689 --> 00:02:21.580 A:middle L:90%
because the input is periodic, you see a periodic
38
00:02:21.590 --> 00:02:24.639 A:middle L:90%
, um, shape in tange off and sign effects
39
00:02:24.639 --> 00:02:28.060 A:middle L:90%
, and that's basically what's happening here. Let's see
40
00:02:28.060 --> 00:02:30.860 A:middle L:90%
what happens if we use a very large number.
41
00:02:30.240 --> 00:02:35.150 A:middle L:90%
For example, 10 factorial. You can see that
42
00:02:35.150 --> 00:02:38.060 A:middle L:90%
the blocks are going to be almost perpendicular right here
43
00:02:38.069 --> 00:02:42.189 A:middle L:90%
, and of course it's not. But I can
44
00:02:42.189 --> 00:02:45.139 A:middle L:90%
imagine that these kind of functions can be very useful
45
00:02:45.139 --> 00:02:47.919 A:middle L:90%
for things such as engineering's and stuff. So I
46
00:02:47.919 --> 00:02:53.259 A:middle L:90%
come from a mathematics or statistics backgrounds, but so
47
00:02:53.259 --> 00:02:55.129 A:middle L:90%
I've never really worked with this particularly, but I
48
00:02:55.129 --> 00:02:59.129 A:middle L:90%
think it's a really cool function. So this is
49
00:02:59.129 --> 00:03:01.150 A:middle L:90%
how can of Ensign of X behaves.