- 1 year ago
Category
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LearningTranscript
00:00:00to 3.30 p.m.
00:00:04Today, we will continue until 8.30 p.m.
00:00:08Is it 8.30 p.m.?
00:00:10I said 8.30 p.m. or 8.00 p.m.?
00:00:12It's 8.00 p.m.
00:00:18Let's start.
00:00:23Continue.
00:00:24First,
00:00:30Hurry up.
00:00:34Since we started in the morning,
00:00:36the 11th question has 30 points.
00:00:40We can see that during the COVID-19 era,
00:00:42there were only one question
00:00:44with 30 points.
00:00:46This is the real thing.
00:00:48It will be difficult for them to write
00:00:50because they need more details.
00:00:52First, they asked
00:00:54to find all the points
00:00:56that make G not continue
00:00:58by asking Tx and A.
00:01:00First, they didn't continue
00:01:02because
00:01:04the domain can't be found
00:01:06at 3.00.
00:01:08So, we will give a reason
00:01:10that F doesn't continue
00:01:12because
00:01:16Tx is at 3.00
00:01:18because
00:01:20it's not
00:01:24on the domain
00:01:26of G.
00:01:28It's not on the domain
00:01:30of Tx.
00:01:32Don't forget to think about the domain.
00:01:48Next, we will
00:01:50think
00:01:52about
00:01:54the negative 1.
00:01:56Think about the negative 1.
00:01:58Think about x
00:02:00and negative 1.
00:02:02How many do you think?
00:02:04Three.
00:02:06The first one is f negative 1.
00:02:08No, g negative 1.
00:02:10This one is g.
00:02:14g negative 1.
00:02:18Which function does g negative 1 use?
00:02:20The function above
00:02:22is 1 divided by
00:02:24negative 1 plus 3.
00:02:26So, it's 2.
00:02:28So, it's 1 divided by 4.
00:02:30The answer is
00:02:34limit x goes to
00:02:36negative 1 on the left of gx.
00:02:44Which function does
00:02:46negative 1 on the left use?
00:02:50The function above
00:02:52is the same.
00:02:58It's 1 divided by 4.
00:03:02Next, limit x goes to
00:03:04negative 1 on the right of gx.
00:03:12I don't think so.
00:03:14Negative 1 on the left
00:03:16is less than negative 1.
00:03:20That's right.
00:03:24Negative 1 on the left
00:03:26is less than negative 1.
00:03:28Negative 1 on the left
00:03:30is less than
00:03:320.9999.
00:03:40No.
00:03:42It's more than 1.
00:03:44That's right.
00:03:46I'm confused.
00:03:50Negative 1 on the right
00:03:52is less than
00:03:540.999.
00:03:56That's right.
00:03:58Negative 1 on the right
00:04:00is 3 divided by 4
00:04:02minus x.
00:04:043 divided by 4 minus 1
00:04:06is
00:04:107 divided by 4.
00:04:127 divided by 4.
00:04:14The third equation.
00:04:16This means
00:04:18g minus 1
00:04:20is equal to the limit.
00:04:26But it's not equal to the limit
00:04:28x goes to negative 1 on the right
00:04:30of gx.
00:04:321 divided by 4 is equal to 1 divided by 4.
00:04:34It's not equal to 7 divided by 4.
00:04:40I'm confused.
00:04:44I feel sorry for my friend.
00:04:48Wait.
00:04:56Wait.
00:04:58Do you know your friend?
00:05:00You don't know him, right?
00:05:02Come this way.
00:05:04Let your friend sit here.
00:05:06It won't be blocked.
00:05:08Your friend is about 2 meters tall.
00:05:14You can sit inside.
00:05:18That's right.
00:05:20That's right.
00:05:26Calm down.
00:05:28Calm down.
00:05:46gx is not equal to
00:05:48gx is equal to negative 1.
00:05:50It means
00:05:52gx is equal to negative 1
00:05:54is
00:05:56not related
00:06:00to
00:06:04not related
00:06:06to
00:06:08jump
00:06:10When you write an equation,
00:06:12you have to write it in detail.
00:06:14Where does it come from?
00:06:16and
00:06:18not related to
00:06:20Let me think.
00:06:26Let me think.
00:06:36Actually,
00:06:38you can write it deeper.
00:06:40It's not related to
00:06:42what?
00:06:44removable.
00:06:46You can think about 3 more things.
00:06:48If it's 30 points,
00:06:50write it as much as possible.
00:06:52Think about x
00:06:54is equal to
00:06:56x is equal to
00:06:58x is equal to 2
00:07:00x is equal to 2
00:07:02Think about x is equal to 2.
00:07:06Which function does
00:07:08f2 use?
00:07:14f2
00:07:163 over 4 minus
00:07:183 over 4 minus 2
00:07:203 minus
00:07:228 over 4
00:07:26minus 5 over 4
00:07:302 limit x to
00:07:322 on the left of fx
00:07:36Which function does
00:07:382 on the left use?
00:07:42less than 2
00:07:463 over 4 minus x
00:07:48minus 5 over 4
00:07:523 limit x to
00:07:542 on the right
00:08:043 over 3
00:08:083 over 5
00:08:103
00:08:18f2
00:08:20is equal to
00:08:22limit on the left
00:08:26but not equal to
00:08:28limit on the right.
00:08:32minus 5 over 4
00:08:34minus 5 over 4
00:08:36but not equal to
00:08:38limit on the right.
00:09:08gx is not continuous
00:09:14at x is equal to 2
00:09:16at x is equal to 2
00:09:18is not continuous
00:09:20at x is equal to 2
00:09:22at x is equal to 2
00:09:24at x is equal to 2
00:09:26cannot jump
00:09:28cannot jump
00:09:30cannot jump
00:10:00there is no more 30 points
00:10:02there is no more 30 points
00:10:04we will reduce the points
00:10:06it's too much
00:10:10one point is gone
00:10:12right?
00:10:24one in your heart
00:10:30ok
00:10:32are you ready?
00:10:36no need
00:10:38enough
00:10:40it's ok
00:10:42if you want to write
00:10:44there are 3 points
00:10:46that are not continuous
00:10:48no need
00:10:50I have concluded
00:10:52g is not continuous
00:10:54right?
00:11:12minus 3
00:11:14minus 1
00:11:16minus 3
00:11:18minus 1
00:11:24We have to add it in the first domain, but we don't have to fix it here.
00:11:32Because these points are not continuous.
00:11:42No, wait a minute, let me think.
00:11:48No, wait a minute, let me think.
00:11:55We don't have to fix it.
00:11:57Because I said it again, why don't we have to fix it?
00:12:02Because at g-1 it can think, but it's just not equal to the limit.
00:12:05For example, it is still in the domain, but the line is just separated from each other.
00:12:11Do you understand? But the black dot is still there.
00:12:15But if g-1 can't think of it at all, it has to be fixed in the domain as well.
00:12:21Suppose you can't find the value at g-1, you have to fix it in the domain, so you don't have to fix it.
00:12:27Because g-1 and g-2 can be found, right?
00:12:31What g can find is useful, it can be in the domain.
00:12:35I'm going to fix it, I'm going to make a mistake.
00:12:41That's right.
00:12:51So you don't have to fix it in the domain, unless g-1 can't find the value.
00:12:55Then fix it in the domain above.
00:13:05Next is the derivative.
00:13:15Go to the div.
00:13:17Have you ever done this?
00:13:21How do you do this?
00:13:23They give the data, see?
00:13:25Do you want to ask the derivative?
00:13:29f-dot-g is f-minus-g.
00:13:31Div and replace the third value.
00:13:33Don't just look at this expression.
00:13:35Just look at this expression.
00:13:37front
00:13:39rear
00:13:41plus rear
00:13:43front
00:13:45What is the front?
00:13:47f-3, right?
00:13:49This is the front, rear, plus rear, front.
00:13:51The derivative.
00:13:53f-3 is 7.
00:13:57g-3
00:13:59minus 1
00:14:01g-3
00:14:03minus 4
00:14:05f-3
00:14:07minus 4
00:14:09The derivative.
00:14:11minus 7 plus 16
00:14:13The answer is
00:14:159
00:14:17dot e
00:14:239 dot e
00:14:259 dot e
00:14:279 dot e
00:14:299 dot e
00:14:319 dot e
00:14:339 dot e
00:14:359 dot e
00:14:379 dot e
00:14:399 dot e
00:14:419 dot e
00:14:43Next, question 2.
00:14:45Ask g-dip-4.
00:14:47How much is it?
00:14:49It's very easy, g-dip.
00:14:51It's a dip.
00:14:53g-dip
00:14:554 divided by 32
00:14:57x to the power of 3 plus 10x
00:14:598 times 4 is 32
00:15:011 divided by 8
00:15:03x to the power of 3 plus 10x
00:15:05Replace 4 with
00:15:071 divided by 8
00:15:094 to the power of 3 plus
00:15:1110 to the power of 4
00:15:134 to the power of 3
00:15:15is 12
00:15:174
00:15:1916
00:15:21not 12
00:15:234
00:15:2564
00:15:2764 divided by 8
00:15:29plus 40
00:15:318 times 8 is 64
00:15:3348
00:15:35The answer is d-dot.
00:15:37Yeah
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00:19:21Divide by the x, ok.
00:19:25Divide by the x.
00:19:39Move to the right.
00:19:41Delete the y and add the x.
00:19:45Delete and add.
00:19:482y cos 2x.
00:19:53Divide by the x.
00:19:57x cos y plus cos 2x.
00:20:07Move to the right.
00:20:11Divide by the x.
00:20:17x cos y plus cos 2x.
00:20:23Move to the left.
00:20:25Delete and add.
00:20:27x cos y plus cos 2x.
00:20:29Move to the right.
00:20:31Delete and add.
00:20:33x cos y plus cos 2x.
00:20:35Is there a choice?
00:20:37Ask the truth.
00:20:472y cos 2x.
00:20:51Where is my y?
00:20:53There is no answer.
00:21:03There is no answer.
00:21:11There is no answer.
00:21:13The answer is e.
00:21:17There is no y sign in this.
00:21:29There is no y sign in each choice.
00:21:33There is no y sign in any of the choices.
00:21:37There is no y sign in any of the choices.
00:21:47There is no y sign in any of the choices.
00:21:55There is no y sign in any of the choices.
00:21:57There is no y sign in any of the choices.
00:21:59There is no y sign in any of the choices.
00:22:09The answer is d.
00:22:11The answer is d.
00:22:13The answer is d.
00:22:15The answer is d.
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00:22:51Answer
00:22:55What?
00:22:59Start
00:23:01Dip lock u base a
00:23:03The formula is
00:23:051 part u
00:23:071 part u
00:23:13Why is pen missing?
00:23:151 over u, a is 6 and dip u is 3x2, the answer is a.
00:23:2910 seconds is too long for this question, isn't it?
00:23:38You don't have to touch it, there's already a choice. Pass.
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00:24:22Answer
00:24:29OMG
00:24:32You can dip r cross.
00:24:361 minus
00:24:39root
00:24:411 minus u power 2
00:24:451 minus u power 2
00:24:47and dip u, dip on u is 1 over u
00:24:51and dip u is 4
00:24:544 minus 4?
00:24:564 minus 4, what's the answer?
00:25:00The answer is b.
00:25:07OMG
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00:25:36You have 3 minutes.
00:25:426, 3 minutes, start.
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00:45:05and he wrote it as an opening sentence, please tell the TA to correct it.
00:45:13Correct it a little bit.
00:45:18How much can you dip once?
00:45:211 over 2, x is decreasing, 1 over 2.
00:45:251 over 2, is it root x?
00:45:28But this one, x must be greater than anything else.
00:45:32More than 0, because it's under the root, right?
00:45:36And 0 can't be 0 either, this must be greater, this is greater than or equal to, this is greater.
00:45:40Which this differentiable, this dip, it takes the opening sentence.
00:45:44It doesn't count the number 0, so it's okay.
00:45:47F can be found.
00:45:54On the opening sentence.
00:46:03Can I not think of these?
00:46:06Can I think of the value of c?
00:46:09Because these must be obtained anyway, right?
00:46:12Not always, there are choices.
00:46:16See, there are good choices too.
00:46:19If these two are not obtained, one will answer e immediately.
00:46:22That is, there is no value of c.
00:46:25It's all trapped.
00:46:27How many values of c will there be?
00:46:30At least one value.
00:46:33On the opening sentence.
00:46:360, 4.
00:46:39Which makes
00:46:42f'c equal to
00:46:49f or 0?
00:46:52f or 0?
00:46:54f or 0?
00:46:57fb
00:47:00minus fa
00:47:03divided by b minus a.
00:47:07ba is 40.
00:47:10b is 4, a is 0.
00:47:17f'c has just been dipped.
00:47:19f'c has just been dipped.
00:47:221 over 2 root 4
00:47:25is equal to f4.
00:47:291 over 2 root 4
00:47:32minus f0.
00:47:351 over
00:47:38No, it's not.
00:47:41Root 4 minus
00:47:44root 0.
00:47:47Divide by
00:47:494 minus 0.
00:47:521 over 2 root 4 is equal to
00:47:552 over 4.
00:47:581 over 2.
00:48:012 root 4 is equal to 2.
00:48:04Root 4 is 1.
00:48:07It means that 4 is equal to
00:48:10Huh?
00:48:13Is there a minus sign?
00:48:16It can't be a minus sign.
00:48:20Right?
00:48:23It's not plus or minus 1.
00:48:25It's 4 equal to 1.
00:48:28Is 4 equal to 1 in the opening sentence?
00:48:30Is it 0, 4?
00:48:32Yes, it is. There must be a value 1.
00:48:36But what is the choice?
00:48:40It should be 0.
00:48:42So we have to replace 4 with 1.
00:48:44Replace 4 with 1
00:48:46in x value.
00:48:49In y and root x.
00:48:52We get y equal to root 1.
00:48:54It's the same.
00:48:56We get 1.
00:48:58So it's a pair of 1 and 1.
00:49:00It's a pair of x and y.
00:49:06It's a formula.
00:49:09It's like a formula.
00:49:14Answer A.
00:49:204 is x value.
00:49:22Normally, it's root x.
00:49:24It's root here.
00:49:26We just replace x with c.
00:49:28Let's find y value.
00:49:30What?
00:49:32No.
00:49:34I told you to choose half.
00:49:36Oh.
00:49:44I'll take a break.
00:49:46I'll stop at 8 p.m.
00:49:52Question 10.
00:49:54I'll take a break at 5 p.m.
00:49:56Question 10.
00:50:04Let me see.
00:50:06When should I take a break?
00:50:10I'll take a break at 5 p.m.
00:50:123 more questions.
00:50:16I've never done this question before.
00:50:18Let me see.
00:50:20The oil tank
00:50:22has 6 holes.
00:50:26Why is it so hard to read?
00:50:28The oil tank
00:50:30has 6 holes.
00:50:32The oil tank
00:50:34has 6 holes.
00:50:36It's a circle.
00:50:42The oil tank
00:50:44has 6 holes.
00:50:46It's a circle.
00:50:48It's a circle.
00:51:00It has 6 holes.
00:51:06It's a circle.
00:51:08It's a circle.
00:51:10How did he draw a circle?
00:51:12That's cool!
00:51:16So, the oil tank didn't do anything with this question.
00:51:19If you're interested in this circle.
00:51:23Actually, the oil tank I drew didn't use it at all.
00:51:27How many feet per second does a circle have?
00:51:32Which has a radius
00:51:34dr by dt equals 2 feet per second.
00:51:40Let's find out how much the area will increase with the value
00:51:47dr by dt
00:51:50will be equal to when there is a radius equal to 60 feet.
00:51:54In conclusion, the oil tank can be omitted.
00:51:58Right?
00:52:00He didn't use it at all.
00:52:02He was interested in the area of this circle.
00:52:04He didn't touch the oil tank at all.
00:52:06See?
00:52:08So, let's define the area of the circle first.
00:52:17What do we need?
00:52:19The area is the area of the oil tank.
00:52:32The circle is too big.
00:52:35The radius is the time.
00:52:37The values are the values.
00:52:39The time is the second.
00:52:41r is the radius.
00:52:43The radius of the oil tank is...
00:52:47The radius is the foot.
00:52:55So, the circle is...
00:52:57The circle is the radius.
00:52:59The radius is the foot.
00:53:01The radius is the radius.
00:53:03What is the formula for the circle area?
00:53:08It's the most difficult one. Area is equal to 2πr.
00:53:16dA by dt is equal to 2πr dA by dt.
00:53:20I can't solve it. It's too easy.
00:53:25dA by dt is equal to 60.
00:53:44Wait, it's not 60.
00:53:46Find the area of the circle.
00:53:52dA by dt is equal to 2πr dA by dt.
00:53:59Find the area of the circle.
00:54:05dA by dt is equal to 2πr dA by dt.
00:54:10The answer is 240π.
00:54:16The unit is the foot per second.
00:54:22Find the area of the circle.
00:54:52Find the area of the circle.
00:55:22Find the area of the circle.
00:55:52Find the area of the circle.
00:56:22Find the area of the circle.
00:56:52Find the area of the circle.
00:57:22Find the area of the circle.
00:57:52Find the area of the circle.
00:58:22Find the area of the circle.
00:58:52Find the area of the circle.
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00:59:32Find the area of the circle.
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01:03:40Find the area of the circle.
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01:08:54Find the area of the circle.
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01:10:42Find the area of the circle.
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