WEBVTT
1
00:00:00.940 --> 00:00:03.850 A:middle L:90%
So here the function that we're given is the limit
2
00:00:04.240 --> 00:00:06.139 A:middle L:90%
. As X approaches zero from the right of the
3
00:00:06.139 --> 00:00:09.689 A:middle L:90%
tangent of two X. Raised to the power of
4
00:00:09.699 --> 00:00:14.000 A:middle L:90%
acts. We're going to want to rewrite this by
5
00:00:14.000 --> 00:00:17.179 A:middle L:90%
taking the natural log of both sides. Um and
6
00:00:17.179 --> 00:00:18.420 A:middle L:90%
the reason why we do this is so we can
7
00:00:18.420 --> 00:00:22.059 A:middle L:90%
rewrite it now as the natural log of your tangent
8
00:00:22.070 --> 00:00:28.600 A:middle L:90%
of two x Divided by one over X. Now
9
00:00:28.600 --> 00:00:31.519 A:middle L:90%
with this, when we take the limit we get
10
00:00:31.530 --> 00:00:33.990 A:middle L:90%
negative infinity over infinity. So we're gonna have to
11
00:00:33.990 --> 00:00:37.439 A:middle L:90%
use low tells rule. Taking the derivative of the
12
00:00:37.439 --> 00:00:40.810 A:middle L:90%
top and bottom. We end up getting a negative
13
00:00:40.820 --> 00:00:52.049 A:middle L:90%
two X squared second squared two X over signed to
14
00:00:52.049 --> 00:01:02.140 A:middle L:90%
Acts over Crossan Q. Acts that allows us to
15
00:01:02.140 --> 00:01:07.609 A:middle L:90%
cancel some things um and simplify further. Um Ultimately
16
00:01:07.609 --> 00:01:08.569 A:middle L:90%
though, when we apply the limit will get the
17
00:01:08.569 --> 00:01:11.469 A:middle L:90%
indeterminate form again. So we have to take the
18
00:01:11.469 --> 00:01:14.390 A:middle L:90%
derivative one more time. And that will give us
19
00:01:15.239 --> 00:01:23.670 A:middle L:90%
negative for X. Over to co sign two X
20
00:01:23.439 --> 00:01:26.730 A:middle L:90%
. Now, when we apply the limit is exposed
21
00:01:26.739 --> 00:01:30.459 A:middle L:90%
zero, we get zero. So we see that
22
00:01:30.459 --> 00:01:34.480 A:middle L:90%
the natural log of Y equals zero, which means
23
00:01:34.480 --> 00:01:37.680 A:middle L:90%
that why is going to equal one for the final
24
00:01:37.680 --> A:middle L:90%
answer?