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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:15:28
The factorized one
1
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:15:40
It’s easier to plug in numbers on calculator
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:16:18
Is this the right way of factorized version ?
https://cdn.discordapp.c…482/IMG_3122.png
IMG_3122.png
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:16:26
https://cdn.discordapp.c…3594/unknown.png
unknown.png
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:17:05
exactly this 👍
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:17:10
Why is there a k ?
1
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:17:55
Ummm I don’t think I’ve seen this before
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:18:21
is just an arbitrary number denoted by k. the thing is the left hand side of the equation is equal to the right hand side (RHS) but the RHS is incredibly more difficult to compute in a calculator
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:19:03
yes this is entirely correct
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:19:56
If I want to put it in calculator, do I have to manually count the top then bottom then the whole radical or can I just type everything in?
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:22:09
you can just type everything in, but be careful you could make a mistake if you type so much digits operations without a "checkpoint".
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:23:25
If I want to be extra careful and want to type one by one, for the inside radical first, should I type 2(y-yo) divided by -g or the other way around ?
1
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:26:41
this one ( 2(y-yo)) because if you use this (2y-2yo) you could make the following mistake (extremely common) 2y-2y0/-g that is $$2y-\frac{2y_{0}}{-g}$$ instead of what you want $$\frac{2y-2y_{0}}{-g}$$
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
510,789,298,321,096,700
TeXit
11/07/2021 17:27:30
**BillyElKid**
https://cdn.discordapp.c…502881878148.png
738072502881878148.png
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:29:15
Oh I meant it this way
1
0
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:29:19
https://cdn.discordapp.c…630/IMG_3124.png
IMG_3124.png
1
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:29:58
aaaa sorry i'm dumb
0
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pandora ୨୧
5555
pandora ୨୧
false
868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:30:00
Like if I want to solve it one by one instead of typing the whole radical into calculator (because sometimes accident lack of bracket can change the whole answer)
1
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BillyElKid
9891
BillyElKid
false
868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:30:02
Nono
1
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BillyElKid
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BillyElKid
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:30:05
:p
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:30:49
i would prefer the second one, but both ways seems fine to me
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pandora ୨୧
5555
pandora ୨୧
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:31:49
I see I see
1
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:31:52
Also
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:31:55
https://cdn.discordapp.c…500/IMG_3125.png
IMG_3125.png
1
0
null
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:32:02
The negative must put inside the radical?
1
0
611,787,651,661,561,900
pandora ୨୧
5555
pandora ୨୧
false
868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:32:51
Every time when you root something, the negative and plus sign has to be all inside the radical or does it matter ?
1
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help-10
f0b0029cde9b49dea1985582cb6b7abb
738,072,502,881,878,100
BillyElKid
11/07/2021 17:35:59
yes it is extremely important with the negative ( the positive is indifferent), because this expression $$\frac{2(y-y_{0})}{g}$$ is negative for the context of your problem (i assume free fall or something like physics), so try to calculate the radical of -2 in your calculator.
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help-10
f0b0029cde9b49dea1985582cb6b7abb
510,789,298,321,096,700
TeXit
11/07/2021 17:36:03
**BillyElKid**
https://cdn.discordapp.c…502881878148.png
738072502881878148.png
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:36:45
Yes it is for finding time in a free fall question!
1
0
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help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:37:51
Alright I finally understand this question
1
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:38:36
Thank you so much for your time to try understand and guide me through, I really appreciate the explanations! (:
1
0
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868
help-10
f0b0029cde9b49dea1985582cb6b7abb
611,787,651,661,561,900
pandora ୨୧
11/07/2021 17:39:15
.close
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869
help-10
3fbfeb7383494c959ec4558c912584e2
928,520,037,269,131,300
hellomeow
02/23/2022 23:55:02
How come x = 4y 6y + x/2 = 212 isnt right?
https://cdn.discordapp.c…3364/unknown.png
unknown.png
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869
help-10
3fbfeb7383494c959ec4558c912584e2
521,464,336,284,254,200
Gamer Dio
02/23/2022 23:58:13
Looks right to me
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help-10
3fbfeb7383494c959ec4558c912584e2
928,520,037,269,131,300
hellomeow
02/24/2022 00:00:15
Oh ok cuz the answers on google said it was 6x + y/2 = 212 so i was confused
1
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869
help-10
3fbfeb7383494c959ec4558c912584e2
521,464,336,284,254,200
Gamer Dio
02/24/2022 00:01:04
They just used different letters. y = 4x and 6x + y/2 = 212. They're identical in meaning
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869
help-10
3fbfeb7383494c959ec4558c912584e2
928,520,037,269,131,300
hellomeow
02/24/2022 00:01:44
Ohh
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help-10
3fbfeb7383494c959ec4558c912584e2
928,520,037,269,131,300
hellomeow
02/24/2022 00:02:05
but the way they solved it they did some let statement saying x was the bigger number and y was the smaller number
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869
help-10
3fbfeb7383494c959ec4558c912584e2
928,520,037,269,131,300
hellomeow
02/24/2022 00:02:24
but when it said "six times the smaller number" they put 6x
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help-10
1a7231b967374838bd43c176e1c79ead
725,233,098,115,252,200
The Real Thing
02/24/2022 01:00:08
https://cdn.discordapp.c…8122/unknown.png
unknown.png
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870
help-10
1a7231b967374838bd43c176e1c79ead
725,233,098,115,252,200
The Real Thing
02/24/2022 03:24:23
.close
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:25:58
https://cdn.discordapp.c…9696161792/1.PNG
1.PNG
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:26:02
hi for 9f)
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:26:14
Could someone tell me what im doing wrong
1
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:26:39
I wrote the derivative of f) and got (x^1/2) / (x^1/3)
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871
help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:26:45
and subsituted 1
1
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871
help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:26:50
and i got the wrong answer so
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:28:59
@Helpers
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:29:13
i tooked derivative to help me find m
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871
help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
220,517,274,845,577,200
ramonov
02/24/2022 03:34:23
show work for your derivative
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:48:12
https://cdn.discordapp.c…E62EBCC1C3F5.jpg
3C31CF57-8466-45BB-8B40-E62EBCC1C3F5.jpg
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:48:14
If u could point my mistake b rly nice
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
312,175,417,085,788,160
conan
02/24/2022 03:49:26
you could split it up as $y=\frac{\sqrt{x}}{\sqrt[3]{x}}-\frac{2}{\sqrt[3]{x}}$
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
510,789,298,321,096,700
TeXit
02/24/2022 03:49:28
**worm**
https://cdn.discordapp.c…417085788171.png
312175417085788171.png
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
312,175,417,085,788,160
conan
02/24/2022 03:49:37
try doing the derivative again
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
312,175,417,085,788,160
conan
02/24/2022 03:50:12
also you can't take the derivative of the numerator and the denominator separately you have to either combine it or use the quotient rule
0
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871
help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:50:37
ohh okok
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
922,127,699,181,436,900
<Chaos/>
02/24/2022 03:51:36
you need to know X ?
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help-10
f5c4b59b358a4337a458e3cb3b4fdbd4
227,127,566,744,551,420
DellCurry
02/24/2022 03:53:01
i wanted to know x to find m
1
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help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:03:24
But then I can't get into here
https://cdn.discordapp.c…034/IMG_2096.png
IMG_2096.png
1
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help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:04:20
I don't know which inequality i have to use in order to prove part a of the question
1
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help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:19:38
@Helpers
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help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 04:24:16
the mean value theorem is useful here
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help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:25:22
So I take derivatives of arctanu/u w.r.t. u?
1
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help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 04:26:32
hm, I was thinking just using the MVT for arctan(u)
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help-10
bb741a04c535410fa2ae5f894a60502a
880,503,100,711,010,300
Rylo
02/24/2022 04:26:44
a = arctan(u) da/du = lhs da/du < a/tan(a) < 1 that’s just first thoughts and stuff?
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help-10
bb741a04c535410fa2ae5f894a60502a
880,503,100,711,010,300
Rylo
02/24/2022 04:27:01
do you reckon we could prove that tho?
0
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help-10
bb741a04c535410fa2ae5f894a60502a
880,503,100,711,010,300
Rylo
02/24/2022 04:27:03
idk
0
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help-10
bb741a04c535410fa2ae5f894a60502a
880,503,100,711,010,300
Rylo
02/24/2022 04:27:32
ahhh
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help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 04:27:43
for some $a\in(0,u)$ $$\frac{\arctan{u}-\arctan{0}}{u-0}=\frac{1}{1+a^2}$$
0
1
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null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
510,789,298,321,096,700
TeXit
02/24/2022 04:27:46
**dino**
https://cdn.discordapp.c…240898789376.png
328019240898789376.png
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1
null
null
null
null
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872
help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 04:28:12
that works for your proof
0
1
null
null
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872
help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 04:28:31
(assuming that the derivative for arctan is given)
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872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:28:58
Ok let me try it
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 04:29:00
Thanks
1
0
940,283,798,782,894,100
parameters
9023
parameters
false
872
help-10
bb741a04c535410fa2ae5f894a60502a
328,019,240,898,789,400
dino dik
02/24/2022 05:14:56
@parameters how's it going?
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 05:17:21
I am not quite sure about arctan0
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 05:17:35
Is that only one unique solution?
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 05:29:33
Just take it =0 is ok
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 05:50:07
https://cdn.discordapp.c…653/IMG_2098.png
IMG_2098.png
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 05:50:21
Ok let me try try
1
0
328,019,240,898,789,400
dino dik
9674
dino
false
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:52:36
I think I got stucked
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:52:48
So my argument is as follows
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:53:36
Let f(x)=arctan(x) be a cont. function on (0,u)
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:53:58
f'(x)=1/(x^2+1)
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:54:14
And hence f'(a)=1/(a^2+1)
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:54:21
For a>0
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:54:32
Then by LMVT,
1
0
940,283,798,782,894,100
parameters
9023
parameters
false
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:55:45
There exists some real number a belongs to (0,u) such that (f(u)-f(0))/(u-0)=f'(a)
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:56:27
And we have: (arctan(u))/u=1/(a^2+1)
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 08:57:42
Since 1/(x^2+1) is positive for all x belongs to real, then f(x) is strictly increasing
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 09:00:36
Can anyone tell me how to obtain this?
1
0
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
312,175,417,085,788,160
conan
02/24/2022 09:13:40
random thought but have you thought of uh
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
312,175,417,085,788,160
conan
02/24/2022 09:13:57
a < u from mvt right
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
312,175,417,085,788,160
conan
02/24/2022 09:14:36
then 1+a^2<1+u^2 so 1/(1+u^2)<1/(1+a^2)=(arctan u)/u
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 09:17:21
Oh
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 09:17:31
Yes
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 09:17:40
Lol
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
355,287,686,959,071,200
Trenton
02/24/2022 09:17:50
So similarly for 0
0
1
null
null
null
null
null
872
help-10
bb741a04c535410fa2ae5f894a60502a
940,283,798,782,894,100
parameters
02/24/2022 09:17:57
Umm
1
0
null
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null