WEBVTT
1
00:00:00.540 --> 00:00:03.060 A:middle L:90%
to evaluate this limit, know that we can rewrite
2
00:00:03.069 --> 00:00:08.560 A:middle L:90%
this into limit as X approaches three from the left
3
00:00:09.039 --> 00:00:13.640 A:middle L:90%
of square the vex times we have limits as X
4
00:00:13.640 --> 00:00:18.320 A:middle L:90%
approaches three from the left of one over x minus
5
00:00:18.320 --> 00:00:21.809 A:middle L:90%
three, race to the fifth power. Now from
6
00:00:21.809 --> 00:00:26.710 A:middle L:90%
here we have the square root of three times limit
7
00:00:26.719 --> 00:00:30.750 A:middle L:90%
as X approaches three from the left of one over
8
00:00:30.750 --> 00:00:33.909 A:middle L:90%
x minus three to the fifth power. And from
9
00:00:33.909 --> 00:00:38.450 A:middle L:90%
here, if X approaches three from the left,
10
00:00:38.450 --> 00:00:44.240 A:middle L:90%
then that means that X values are less than three
11
00:00:44.250 --> 00:00:47.899 A:middle L:90%
or that's X less than three. And this would
12
00:00:47.899 --> 00:00:51.950 A:middle L:90%
tell us that x minus three is less than zero
13
00:00:52.340 --> 00:00:55.149 A:middle L:90%
or the value of x minus three is negative.
14
00:00:56.140 --> 00:00:59.880 A:middle L:90%
And so approaching three from the left would tell us
15
00:00:59.880 --> 00:01:04.280 A:middle L:90%
that x minus three is a small negative number and
16
00:01:04.280 --> 00:01:08.060 A:middle L:90%
becomes even smaller when raised to the fifth power.
17
00:01:08.939 --> 00:01:12.959 A:middle L:90%
And so one over the fifth power of x minus
18
00:01:12.959 --> 00:01:19.819 A:middle L:90%
three becomes a very large negative number. And so
19
00:01:19.819 --> 00:01:23.459 A:middle L:90%
this is just square root of three times in negative
20
00:01:23.459 --> 00:01:26.250 A:middle L:90%
infinity, which is the same as negative infinity.
21
00:01:26.640 --> 00:01:30.069 A:middle L:90%
And so the value of the limit will be negative
22
00:01:30.069 --> A:middle L:90%
infinity.