- 9/13/2024
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00:00:30Okay, dear students, I welcome you all to the fourth class of today's session of the
00:00:50Department of Political Science.
00:00:51We have already completed three classes of the Department of Political Science.
00:00:54We have come to the end of the fourth class of the Department of Political Science.
00:00:57The topics under this section of the Department of Political Science, we have already covered
00:01:01them all.
00:01:02Our main target was to study space.
00:01:04Space and space exploration.
00:01:06Calculus.
00:01:07This part is not a basic subject.
00:01:09This was our main target.
00:01:11So, we have already covered space.
00:01:13In the last class, we have covered the seven basic topics of space.
00:01:17So, today we are going to talk about the seven basic topics of space.
00:01:21So, today we are going to see some more basic problems of space.
00:01:27What is space in general?
00:01:29How can we determine the loss of change in space?
00:01:33How can we determine the balance of space?
00:01:35What is the relationship between space and the balance?
00:01:38We have already understood these.
00:01:40So, today we are going to discuss some principles of space.
00:01:45These basic principles will be useful for the various calculations of physics.
00:01:49So, in the last class, I gave you a homework to understand space.
00:01:56I hope you got the homework, right?
00:01:58I hope you got the homework, right?
00:02:01Okay?
00:02:02So, let's see some more problems today.
00:02:06So, I gave you a homework.
00:02:09I told you that you have to understand this function.
00:02:12f of x is equal to x to the power n.
00:02:15I told you that you have to understand this function.
00:02:19The basic principle of space is d dx of f of x is equal to limit h tends to 0, f of x plus h minus f of x divided by h.
00:02:32This is the basic principle of space.
00:02:36So, I told you to do this.
00:02:38I wrote the answer to this.
00:02:41I gave you a homework.
00:02:42This may not be possible.
00:02:45But, the rest may be possible.
00:02:48So, let's see.
00:02:49We will do it in this way.
00:02:51So, we have to find f of x is equal to x to the power n.
00:02:57So, above x plus h, where is x?
00:03:01x plus x is where x is.
00:03:05So, x plus h to the power n.
00:03:10Now, the principle of space is d dx of f of x is equal to limit h tends to 0, f of x plus h minus f of x divided by h.
00:03:28So, limit h tends to 0.
00:03:33Below h, f of x plus h means x plus h to the power n minus f of x.
00:03:43f of x means x to the power n.
00:03:48Now, if x plus h to the power n is equal to h square, then x plus h is equal to h square.
00:03:57Then, you can write x square plus 2x h plus h square.
00:04:03If cube is equal to x plus h to the power cube, then x cube minus 3x square plus 3x h square plus h cube.
00:04:17You can write like this.
00:04:18Similarly, it can be equal to 4 or 5.
00:04:25So, x plus h whole square means a plus b whole square, a plus b cube whole cube.
00:04:31We know this formula.
00:04:33But, a plus b to the power 4, a plus b to the power 5.
00:04:37We do not know these formulas.
00:04:40But, these formulas can also be written.
00:04:42That means, a plus b to the power n.
00:04:47This formula can also be written.
00:04:50We might have seen this in 19th century.
00:04:52The formula of a plus b to the power n, Pascal's tribuse.
00:04:57These formulas were there in 19th century.
00:04:59You might have studied this.
00:05:01If you have not studied, then there is no problem.
00:05:03If you have not studied, then there is no problem.
00:05:06If you have not studied, then there is no problem.
00:05:09I will teach you a formula.
00:05:11I will teach you a formula of dipole expansion.
00:05:14For example, 1 plus x to the power n.
00:05:21I need to write this formula.
00:05:23The formula is 1 plus nx.
00:05:28Then, n minus 1 factorial 2, 2 factorial.
00:05:35Do you know what 2 factorial means?
00:05:382 factorial means 1 plus 2.
00:05:413 factorial means 1 plus 2 plus 3.
00:05:464 factorial means 1 plus 2 plus 3 plus 4.
00:05:53From 1 to 4 factorial, there will be a factor.
00:05:57Then, n minus 1 2 factorial.
00:06:00Then, x square.
00:06:02Then, n minus 1.
00:06:05Now, n minus 2.
00:06:08Then, 3 factorial.
00:06:10Then, x cube.
00:06:12Then, it will continue like this.
00:06:15Then, n minus 1, n minus 2, n minus 3.
00:06:20Then, factorial 4, x to the power 4.
00:06:23It will continue like this.
00:06:24This is the formula of dipole expansion.
00:06:26How did I get this?
00:06:28You will get this.
00:06:29When you do math, there is a chapter on dipole.
00:06:33When you read this chapter, Rakey Bulbhai or Abhidada will teach you this.
00:06:39We know this with confidence.
00:06:42This is a formula.
00:06:44Now, I will try to apply this formula here.
00:06:48How will I try to apply this formula?
00:06:50First, I will take this formula.
00:06:51Look at this formula.
00:06:521 plus something to the power n.
00:06:541 plus something.
00:06:55Here, I have x plus h to the power n.
00:06:58Then, I will do one thing.
00:07:02We will divide right by x to the power n.
00:07:06We divide right by x to the power n.
00:07:10Then, limit h tends to 0.
00:07:14h tends to 0.
00:07:16We divide by x to the power n.
00:07:18If we divide by x to the power n,
00:07:20then x plus h to the power n,
00:07:24we will divide by x to the power n.
00:07:26Then, we can write this once.
00:07:28Now, look at minus.
00:07:29to the power n, x to the power n, x to the power n, x to the power n, x to the power
00:07:47power n minus n.
00:07:56So, x to the power n, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:08:25x by x, 1, 1 plus h by x, h by x to the power n minus 1, and x to the power n h.
00:08:42So, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:09:01h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:09:21to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:09:47limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:10:06tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:10:210, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:10:46h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:11:15to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:11:45limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:12:12tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:12:390, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:13:08h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:13:37to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:14:07limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:14:34tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:15:030, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:15:32h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:16:01to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:16:30limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:16:55tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:17:240, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:17:54h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:18:23to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:18:52limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:19:19tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:19:480, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:20:17h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:20:46to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:21:15limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:21:42tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:22:110, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:22:40h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:23:09to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:23:38limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:24:03tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:24:320, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:25:02h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:25:31to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:26:00limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:26:27tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:26:560, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:27:25h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:27:54to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:28:23limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:28:48tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:29:170, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:29:46h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:30:15to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:30:44limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:31:13tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:31:420, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:32:11h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:32:40to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:33:09limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:33:38tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:34:070, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:34:36h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:35:05to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:35:34limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:36:01tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:36:300, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:36:59h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:37:28to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:37:57limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:38:26tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:38:550, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:39:24h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:39:53to 0.
00:39:54.
00:40:24limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:40:43tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:41:120, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:41:41h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:42:10to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:42:39limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:43:06tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:43:350, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:44:04h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:44:33to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:45:02limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:45:29tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:45:580, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:46:27h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:46:56to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:47:25limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:47:54tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:48:230, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:48:52h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:49:21to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:49:50limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:50:17tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:50:460, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:51:15h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:51:44to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:52:13limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:52:42tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:53:110, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:53:40h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:54:09to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:54:38limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:55:07tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:55:360, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:56:05h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:56:34to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:57:03limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:57:32tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
00:58:010, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
00:58:30h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
00:58:59to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
00:59:28limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
00:59:55tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:00:240, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:00:53h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:01:22to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:01:51limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:02:16tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:02:450, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:03:14h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:03:43to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:04:12limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:04:38tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:05:060, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:05:36h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:06:05to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:06:35limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:07:00tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:07:280, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:07:58h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:08:27to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:08:56limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:09:23tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:09:520, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:10:21h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:10:50to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:11:19limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:11:44tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:12:130, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:12:42h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:13:11to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:13:40limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:14:05tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:14:340.
01:15:05limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:15:29tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0.
01:15:58limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:16:25tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:16:540, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:17:23h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:17:52to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:18:21limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:18:50tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:19:190, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:19:48h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:20:17to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:20:46limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:21:11tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:21:400, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:22:05h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:22:32to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0,
01:23:01limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h
01:23:26tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to
01:23:550, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit
01:24:24h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends to 0, limit h tends
01:24:53to 0, sin inverse 3 x square. Therefore, a d dx ln 2 x e to the power 3 x.
01:25:45Therefore, a d dx ln 2 x e to the power 3 x e to the power 3 x.
01:26:14Therefore, a d dx ln 2 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the
01:26:44power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:27:14the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:27:443 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:28:14the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:28:313 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:28:39the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:28:513 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:28:59the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:29:133 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:29:29the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:29:443 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:29:59the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:30:143 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:30:29the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:30:443 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:30:59the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:31:143 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:31:29the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:31:413 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:31:49the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:32:043 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:32:19the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:32:343 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:32:49the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:33:043 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:33:19the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:33:343 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:33:49the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:34:043 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:34:19the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power
01:34:343 x e to the power 3 x e to the power 3 x e to the power 3 x e to the power 3 x e to
01:34:48the power 2 X d dx e to the power tan 4 X divided by Nietzsche 3 x s square.
01:34:55e to the power tan 4 x divided by 3 x square. Now, by u by v k key u v inverse formatting
01:35:21the equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:35:28key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:35:35equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:35:41key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:35:47equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:35:54key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:36:01equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:36:07key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:36:13equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:36:20key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:36:27equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:36:34key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:36:41equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:36:48key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:36:55equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:37:02key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:37:09equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:37:16key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:37:23equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:37:30key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:37:37equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:37:44key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:37:51equation. So, by u inverse key u inverse formatting the equation. So, by u inverse
01:37:58key u inverse formatting the equation. So, by u inverse key u inverse formatting the
01:38:05equation.
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