WEBVTT
1
00:00:01.320 --> 00:00:03.629 A:middle L:90%
and this problem, we want to prove or disprove
2
00:00:03.629 --> 00:00:07.000 A:middle L:90%
the claim. The limit is X approaches. Zero
3
00:00:07.839 --> 00:00:11.060 A:middle L:90%
of the function of X equals a squared of x
4
00:00:11.400 --> 00:00:17.589 A:middle L:90%
zero. So let's consider the graph of X equals
5
00:00:17.589 --> 00:00:21.010 A:middle L:90%
the square root of X. Here, to the
6
00:00:21.010 --> 00:00:28.109 A:middle L:90%
left is a sketch of the novaks. So we
7
00:00:28.109 --> 00:00:35.880 A:middle L:90%
see that if we approach X equals zero from the
8
00:00:35.880 --> 00:00:47.539 A:middle L:90%
right, the graph is getting closer and closer.
9
00:00:49.439 --> 00:00:57.049 A:middle L:90%
Two, sir. Here for the right hand limit
10
00:00:59.740 --> 00:01:06.849 A:middle L:90%
. Zero. However, there is no limit from
11
00:01:06.849 --> 00:01:12.150 A:middle L:90%
the left hand side. So we wondered, Does
12
00:01:12.150 --> 00:01:25.170 A:middle L:90%
this mean that'll limit is undefined? Well, yes
13
00:01:25.170 --> 00:01:30.319 A:middle L:90%
and no. Since the square root of X is
14
00:01:30.319 --> 00:01:40.250 A:middle L:90%
only defined for X values greater than or equal 20
15
00:01:42.739 --> 00:01:51.150 A:middle L:90%
we know that negative numbers are not the domain off
16
00:01:51.150 --> 00:01:57.980 A:middle L:90%
our function. So it's not that the limit doesn't
17
00:01:57.989 --> 00:02:01.742 A:middle L:90%
exactly exist there. It's just totally under find there
18
00:02:04.632 --> 00:02:07.593 A:middle L:90%
. So since X equals zero is an end point
19
00:02:07.082 --> 00:02:10.712 A:middle L:90%
and the limit from the right exists, we know
20
00:02:10.712 --> 00:02:22.633 A:middle L:90%
that the limit has affects approaches. Zero is in
21
00:02:22.633 --> 00:02:24.612 A:middle L:90%
fact, people to zero