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00:00:00อ่ะ วันนี้เป็นสกวิตเทียวเล่มนะครับ
00:00:05สกวิตเทียวเล่มเนี่ยเค้าเรียกว่าธิตดีของการบีบ
00:00:09เราเรียนกับอาจารย์แล้วนะครับ ใกล้จบลิมิตละ
00:00:15สกวิตเทียว...
00:00:19I'm so sorry
00:00:22สกวิตเทียวเล่มหรือว่าธิตดีการบีบเนี่ย บางทีเค้าจะเรียกว่าแซนวิดก็ได้
00:00:28แซนวิดเทียวเล่ม
00:00:34อ๋อ มันก็เหมือนกับการปะกบ เลยว่าแซนวิดก็ได้
00:00:40สื้อขั้นก่อนให้การหกนะครับเนี่ย เค้าบอกว่า ฟังชั่นที่เราจะหาลิมิตมันดันกวดเกวงมากเลย เกวงเป็นแบบไงงี้
00:00:48So, we don't have to think about the function fx, but we can think about the function h, which is a function that is greater than fx
00:01:04Let's think about the function g, which is a function that is less than or equal to fx
00:01:13It means that fx is in the middle, right?
00:01:17fx is in the middle, like this, dx and hx are at the top, this one is at the bottom, this one is at the top, fx is in the middle
00:01:25fx is in the middle, see? dx and hx
00:01:31It is said that the principle is very simple, let's think about the limit of the bottom line and the top line instead
00:01:37If the limit of the bottom line and the top line is equal to l, think of it like this
00:01:42Up and down, it pushes the same value like this
00:01:48And consider that the middle does not have to think, the middle will also be pushed into the same value
00:01:53Can you imagine? It is the theory of pushing
00:01:56And the middle does not have to think, it will be equal to l
00:02:00Most of these are used with nodes
00:02:06The example that is used frequently, such as the limit x goes to t of sin x over x, is the one that is used frequently
00:02:16The first thing we need to know is the top line
00:02:22The top line cannot answer how much it is
00:02:26The top line revolves in a circle, a unit circle
00:02:30It means that the infinity line will be between negative 1 and 1
00:02:34See? The value will be between negative 1 and 1, not more than this
00:02:39The 0th line is 0, the 90th line is 1, right?
00:02:42The 90th line is 1, the 0th line is 0, and the 270th line is negative 1
00:02:50It will be between negative 1 and 1, not more than this
00:02:54Therefore, it is not a unit circle anymore, it becomes a negative 1 unit circle, not a 1 unit circle
00:03:01The number here is twisted, right? It can be negative 1, it can be 1, or it can be 0.5, which the value is a unit circle
00:03:08Therefore, we use the Sqrt Theorem to think
00:03:17The Sqrt Theorem is a simple comparison between sine and sine
00:03:25Sine is not more than negative 1 and 1, right?
00:03:29The sine is not more than negative 1 and 1
00:03:32And the simple comparison is to add x to it
00:03:36It means that the sine of x will be between negative 1 and 1, right?
00:03:49And this is the function g, this is the function f, and this is the function h
00:03:55Oh, it's coming
00:03:58I thought it wouldn't come
00:04:01Oh, the camera is out of focus
00:04:04Wait, let me adjust it
00:04:17It means that I don't have to think about the function f in the middle anymore
00:04:22I think about the function f on the bottom and the function f on the top instead
00:04:25Let's try to think about it
00:04:27The limit x goes to t of negative 1 over x
00:04:31And the limit x goes to t of 1 over x
00:04:37Yesterday I taught you about the limit t, right?
00:04:41What is the value of the unit circle?
00:04:440
00:04:46What is the value of the unit circle?
00:04:480
00:04:50It means that I don't have to think about the function f in the middle anymore
00:04:52If the function f on the bottom is 0
00:04:53The function f on the top is 0
00:04:55It means that I don't have to think about the function f on the top
00:04:57The function f on the middle is a sandwich, right?
00:04:59If I squeeze the sandwich like this, the function f on the middle will be 0
00:05:03It's a paradox, right?
00:05:05So the limit x goes to t of negative 1 over x will be 0
00:05:13So, in this case, we can easily remember that it's used for the quantity of sides and corners
00:05:26It's used for only these two
00:05:29Because the quantity of sides and corners can't be summed up
00:05:33It's a value between negative 1 and 1
00:05:35And we don't know what the value is
00:05:43I'll let my friend do the writing first
00:05:52Who's late?
00:05:54I'll let you sit down first
00:05:56I'm so tired
00:06:07Do it quickly
00:06:13It's a good thing that I told him to go to class at 5 o'clock
00:06:25Because I know that I'll be very late
00:06:31Otherwise, I'll be late for class
00:06:43I'll let you sit down first
00:06:44I'll let you sit down first
00:06:46I'll let you sit down first
00:06:47I'll let you sit down first
00:07:10I'll let you sit down first
00:07:12I'll let you sit down first
00:07:13I'll let you sit down first
00:07:15I'll let you sit down first
00:07:28Most of the time, the squid will hide the values
00:07:32It doesn't like to be its own value
00:07:35It likes to hide
00:07:37If you can't find it, be careful
00:07:39If you can't find it, be careful
00:07:40If you can't find it, be careful
00:07:42If you can't find it, be careful
00:07:44It likes to hide the values
00:07:46Because it can be a limit
00:07:48It will hide the values
00:07:50You have to be careful
00:07:52If you can't find it, be careful
00:07:54If you can't find it, be careful
00:07:59I'll let my friend do the writing first
00:08:10I'll let my friend do the writing first
00:08:35First question
00:08:36The old squid has 5 points
00:08:38This was a story in 1959
00:08:41Let's take a look
00:08:43If you multiply it by 4, it will be 0
00:08:46You get 0
00:08:48Then cross 2 times 0 times 2
00:08:52The cross 2 times 0 times 2
00:08:550 times 2 is not negative, right?
00:08:58It's close to 0
00:09:00Whether left or right, when you multiply it by 2, it's not negative
00:09:03So it will be cross 3
00:09:06So it will be cross 3
00:09:08You can't think of cross 3
00:09:10It's between negative 1 and 1
00:09:12So you have to use the squid theorem
00:09:15I think it's easy
00:09:17I think it's easy
00:09:19Do 1 less than 3 minutes
00:09:21Do 1 less than 3 minutes
00:09:23S-Q-U-E-E
00:09:25S-Q-U-E-E
00:09:26S-Q-U-E-E
00:09:30Start with cross
00:09:31Start with cross
00:09:34When x is a bracket, the cross is between negative 1 and 1
00:09:38Like before
00:09:40And if you want to think of x to the power of 4 times cross
00:09:48It must be between negative x to the power of 4 times x to the power of 4
00:09:53If the cross is between negative 1 and 1
00:09:56The cross must be between negative x to the power of 4 times x to the power of 4
00:09:59This is function d
00:10:01This is function h
00:10:03This is function h
00:10:05Just think of the bottom and top
00:10:19Just think of the bottom and top
00:10:240 to the power of 4
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01:56:55remote air in there.
01:56:56remote air in there.
01:56:57remote air in there.
01:56:58remote air in there.
01:56:59remote air in there.
01:57:00remote air in there.
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01:57:05remote air in there.
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01:57:11remote air in there.
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01:59:12remote air in there.
01:59:13remote air in there.
01:59:14remote air in there.

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