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help-1
9c51a3d4165f492d94483eca2a52e413
348,696,743,388,381,200
A Lonely Bean
01/19/2022 08:43:34
@Moderators
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9c51a3d4165f492d94483eca2a52e413
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 08:43:45
Like when modeling a spring
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help-1
9c51a3d4165f492d94483eca2a52e413
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 08:43:54
That is a real life application
0
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:38:30
solve with induction for all n element of N<0> does it also make sense to just explain it by saying that 1/k will always get smaller and smaller and n/3+1 will only get bigger and bigger so it is solved?
https://cdn.discordapp.c…4318/unknown.png
unknown.png
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help-1
100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:38:59
or is that like not formal mathematical proof?
1
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:40:24
actually I think it looks a bit more complicated than that after giving it a second look
1
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help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:43:06
1/k does get smaller and smaller
0
1
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null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:43:13
but the sum is divergent
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
706,934,233,012,371,600
Ansh_
01/19/2022 09:43:55
"1/k will always get smaller and smaller" is true as k increases from 1 to n but: - 1) the L.H.S. is actually a summation of those __smalls__ and -2) the R.H.S. is fixed as n/3 + 1, so it only changes when you change "n" but that will also add a few more terms to the L.H.S. again
0
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null
null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
706,934,233,012,371,600
Ansh_
01/19/2022 09:44:37
So you never really know until you can give a sure shot effort to establish a clear difference in their growth rate :o
0
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null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:44:55
It does say to use induction
0
1
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null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:45:01
so assume it's true for n
0
1
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:45:10
and try to prove the statement for n+1
0
1
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null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:45:18
then check if a base case is true
0
1
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null
null
null
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205,513
help-1
100428ac07c741e491ab35ee37a7859e
381,524,178,165,039,100
Door 'GG' VB
01/19/2022 09:45:24
and voilà
0
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help-1
100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:46:34
ah right
1
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205,513
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100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:46:46
I'll give it a shot.
1
0
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null
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help-1
100428ac07c741e491ab35ee37a7859e
397,948,499,091,521,540
Rolly
01/19/2022 09:50:11
.close
1
0
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help-1
a78e19aa5c7e48d195f99ac5dc834b1c
616,260,585,759,309,800
Sultan_Pulnejov
01/19/2022 09:52:19
$1+1$
1
0
null
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null
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205,514
help-1
a78e19aa5c7e48d195f99ac5dc834b1c
510,789,298,321,096,700
TeXit
01/19/2022 09:52:21
**CodeSniper**
https://cdn.discordapp.c…585759309844.png
616260585759309844.png
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205,514
help-1
a78e19aa5c7e48d195f99ac5dc834b1c
616,260,585,759,309,800
Sultan_Pulnejov
01/19/2022 09:52:29
.close
1
0
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 10:06:19
Any ideas on how to show that the Newton-method used on the function $f(x) = e^{x^2} - 4$ converges for all starting values $x_0 \neq 0$?
1
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
510,789,298,321,096,700
TeXit
01/19/2022 10:07:38
**mrbrown**
https://cdn.discordapp.c…848122327041.png
145653848122327041.png
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help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 10:08:00
The Newton method is defined as $x_{k+1} = x_k - \frac{f(x_k)}{f'(x_k)}$
1
0
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
510,789,298,321,096,700
TeXit
01/19/2022 10:08:03
**mrbrown**
https://cdn.discordapp.c…848122327041.png
145653848122327041.png
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 11:40:38
Just graphing f(x), we can see it has two roots
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 11:40:38
https://cdn.discordapp.c…9118/unknown.png
unknown.png
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 11:41:30
Since f(0) is equidistant to each root (ie the slope is zero) we can't use NM to find the nearest root
0
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 11:42:40
I might try showing that for the given f(x), $$\lim_{n\to \infty} x_{n+1}-x_n=0$$
0
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
510,789,298,321,096,700
TeXit
01/19/2022 11:42:42
**Taril\_Aran**
https://cdn.discordapp.c…354127069184.png
492892354127069184.png
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
510,789,298,321,096,700
TeXit
01/19/2022 11:43:02
**Taril\_Aran**
https://cdn.discordapp.c…354127069184.png
492892354127069184.png
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 11:59:33
yeah that would be cool
1
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:03:57
@Taril_Aran
1
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help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 12:06:22
If I've got my algebra correct, $x_{n+1}-x_n=-\frac{f(x)}{f'(x)}$
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
510,789,298,321,096,700
TeXit
01/19/2022 12:07:14
**Taril\_Aran**
https://cdn.discordapp.c…354127069184.png
492892354127069184.png
0
1
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help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 12:08:12
nvm I don't actually know where to go from here
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:10:23
yeah i can follow so far
1
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:38:21
i have an idea
0
1
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help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:38:36
but im studying this subject as we speak so im no expert
0
1
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help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:39:22
set f(x)/f'(x) as some function g(x), just for easier notation
0
1
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null
null
null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:39:29
then move it to the other side
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:39:47
solve using a non homogenous recurrence relation formula (i literally learned this today so i have no idea if it actually applies here , but it looks like it does)
0
1
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null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:40:18
then you can input ur values onto the solution, and prove what u must
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 12:41:43
@mrbrown
0
1
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help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:51:04
that sounds good!
1
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:51:19
unfortunately I don't know the non-homogenous-recurrence-relation-formula
1
0
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:52:09
I am kinda annoyed they asked such a question which isn't so easily proovable for us lol
1
0
null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 12:52:30
but it is also no excercise which needs proof. Just need to say "true/false"
1
0
null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 13:11:43
oh if it's a true/false it's much easier
0
1
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null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 13:12:04
FYI "show that ..." usually means "prove"
0
1
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null
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 13:13:38
https://en.wikipedia.org/wiki/Newton%27s_method#Failure_analysis
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 13:13:53
This section has some good heuristics to tell if newton's method will fail
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
492,892,354,127,069,200
Taril_Aran
01/19/2022 13:14:56
Two things to look for are: 1. places where f'(x)=0, since this breaks the formula. 2. Places where x_{n+1} gets further away
0
1
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 13:24:50
https://www.youtube.com/watch?v=EfF_XSEX1Sk&list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2&index=20
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help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 13:25:09
it shouldnt be too hard. I got the hang of it in 15 min after watching this video
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LittleMouse
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LittleMouse
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205,515
help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 13:25:34
prerequisite https://www.youtube.com/watch?v=7mhvA5L7KqY&list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2&index=17
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b855a56fe4c4416ab2a16905fc56ee94
145,653,848,122,327,040
mrbrown
01/19/2022 13:25:41
thank you
1
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
322,422,585,323,290,600
Harsh_
01/19/2022 13:26:02
watch this first , if u dont already know it
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help-1
b855a56fe4c4416ab2a16905fc56ee94
321,445,119,171,756,000
Shuri2060
01/19/2022 15:17:54
@Moderators
0
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help-1
b855a56fe4c4416ab2a16905fc56ee94
150,414,892,225,134,600
RokettoJanpu
01/19/2022 15:18:04
ty
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:27:59
Hey I need help on my trig homework I know how to set it up but then actually doing the problem is confusing me
1
0
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help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:28:46
So, what's the problem?
0
1
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:29:24
I have to solve for the angle (x)
1
0
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:29:28
the image is sending
1
0
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:29:29
https://cdn.discordapp.c…9C8FC285171E.jpg
AA2D2836-559B-4CD8-B412-9C8FC285171E.jpg
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:30:06
I know the hypotenuse and the opposite I don’t know the adjacent or the angle
1
0
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205,516
help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:30:17
Here it is clear that sinx = 19/30, right?
0
1
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:30:26
Yeah
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LittleMouse
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:30:32
wait what
1
0
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help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:30:49
Yeah sorry
1
0
null
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205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:30:56
that’s about as far as I can get
1
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782,087,086,416,461,800
LittleMouse
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205,516
help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:30:58
So therefore x is simply arcsin(19/30)
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1
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:31:17
So the answer is just 19/30?
1
0
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205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:31:39
Don’t I have to put a 1 under the x then use the ^-1^
1
0
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205,516
help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:31:55
In general what you'd write is (-1)^k*arcsin(19/30) + pi*k, but here we want x to be an acute angle
0
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help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:32:03
So arcsin(19/30) will do
0
1
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:32:15
no
0
1
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:32:42
$$\arcsin \equiv \sin^{-1}$$
0
1
null
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null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:32:54
what is arsin
1
0
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
510,789,298,321,096,700
TeXit
01/19/2022 15:32:56
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
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205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:32:59
I know sin
1
0
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:33:09
or what is arcsin
1
0
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
348,696,743,388,381,200
A Lonely Bean
01/19/2022 15:33:09
"inverse" of sin
0
1
782,087,086,416,461,800
LittleMouse
2603
LittleMouse
false
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:33:13
oh ok
1
0
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:33:30
whichever notation you have seen
0
1
null
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null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:33:37
So just that then put 19/30
1
0
782,087,086,416,461,800
LittleMouse
2603
LittleMouse
false
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:33:41
or the button on your calculator
0
1
null
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null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:33:48
**no**
0
1
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:33:48
sin-1 (19/30)
1
0
null
null
null
null
null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:34:11
Does the question not tell you to use a calculator?
0
1
null
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null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:34:20
If not, thats all you put.
0
1
null
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null
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205,516
help-1
e331f382de394ccba4083206a96f3f99
637,070,886,561,775,600
doofy
01/19/2022 15:34:31
it dosnt mention any but I used one for the front page
1
0
null
null
null
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null
205,516
help-1
e331f382de394ccba4083206a96f3f99
321,445,119,171,756,000
Shuri2060
01/19/2022 15:34:49
I think its intended to be calculator.
0
1
null
null
null
null
null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
764,607,901,460,987,900
Eau
01/19/2022 16:16:05
https://cdn.discordapp.c…9286/unknown.png
unknown.png
1
0
null
null
null
null
null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
764,607,901,460,987,900
Eau
01/19/2022 16:18:48
can someone help me with this one. I started to learn this stuff today and I'm having some difficulty...
1
0
null
null
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null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
181,429,204,624,080,900
UtopiaZ814
01/19/2022 16:19:01
think this is a integration by parts
0
1
null
null
null
null
null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
181,429,204,624,080,900
UtopiaZ814
01/19/2022 16:19:41
if you take f = x^2 and g' = a^x
0
1
null
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205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
181,429,204,624,080,900
UtopiaZ814
01/19/2022 16:20:00
so you then work out f' and g
0
1
null
null
null
null
null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
764,607,901,460,987,900
Eau
01/19/2022 16:20:24
ohhh ok got it
1
0
null
null
null
null
null
205,517
help-1
0c95517d5dbf4c58bea90905a96d9d77
764,607,901,460,987,900
Eau
01/19/2022 16:20:37
thnkx
1
0
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