WEBVTT
1
00:00:00.640 --> 00:00:04.009 A:middle L:90%
To evaluate this limit, we first rewrite teacher the
2
00:00:04.009 --> 00:00:08.929 A:middle L:90%
4th power-1. Overtake U-1. Since direct
3
00:00:08.929 --> 00:00:14.900 A:middle L:90%
substitution gives us 1 to the 4th power-1 Over
4
00:00:14.900 --> 00:00:19.260 A:middle L:90%
one K-1 which is just 0/0. An indeterminate
5
00:00:19.260 --> 00:00:25.960 A:middle L:90%
value notes that T to the 4th power-1 over
6
00:00:26.440 --> 00:00:29.920 A:middle L:90%
Take U-1. This is equal to t squared
7
00:00:29.920 --> 00:00:36.740 A:middle L:90%
minus one times t squared plus one over T-1
8
00:00:36.740 --> 00:00:41.259 A:middle L:90%
times T squared plus t plus one. Which is
9
00:00:41.259 --> 00:00:47.859 A:middle L:90%
the same as T-1 times t plus one times
10
00:00:47.859 --> 00:00:53.460 A:middle L:90%
T squared plus one over t minus one times T
11
00:00:53.460 --> 00:00:56.469 A:middle L:90%
squared plus t plus one. Now in here we
12
00:00:56.469 --> 00:01:00.920 A:middle L:90%
can cancel out the T-1 and reduce the expression
13
00:01:00.920 --> 00:01:07.260 A:middle L:90%
into T plus one times T squared plus one over
14
00:01:07.739 --> 00:01:11.150 A:middle L:90%
T squared plus t plus one. And so using
15
00:01:11.150 --> 00:01:17.250 A:middle L:90%
this we have this limit equal to limit as T
16
00:01:17.250 --> 00:01:22.409 A:middle L:90%
approaches one of t plus one times t squared plus
17
00:01:22.409 --> 00:01:26.299 A:middle L:90%
one over t squared plus t plus one which is
18
00:01:26.299 --> 00:01:33.560 A:middle L:90%
just one plus one times one squared plus one over
19
00:01:34.040 --> 00:01:37.250 A:middle L:90%
one squared plus one plus one, which is just
20
00:01:38.340 --> 00:01:41.540 A:middle L:90%
4/3. And so this is the value of the
21
00:01:41.540 --> A:middle L:90%
limit.