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help-10
d8b842f4e0a64afb952cef54909e6d8e
569,167,697,925,898,240
Camilleone
01/30/2022 04:31:07
you need to account for the initial value f(0)
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abs_0
01/30/2022 04:31:44
What’s theta and delta tho
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Ansh_
01/30/2022 04:31:58
there's no delta -_- delta(z) is the change in "z"
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Ansh_
01/30/2022 04:32:59
theta is well defined above ^ I suppose.. the angle between the +ve x-axis and the secant
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abs_0
01/30/2022 04:33:25
Well like
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d8b842f4e0a64afb952cef54909e6d8e
307,070,375,735,459,840
abs_0
01/30/2022 04:33:34
The slope of the secant is delta y over delta x
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1
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help-10
d8b842f4e0a64afb952cef54909e6d8e
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abs_0
01/30/2022 04:33:44
So then delta y = that stuff
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abs_0
01/30/2022 04:33:49
Oh that is what you’re saying
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abs_0
01/30/2022 04:33:56
Lol
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d8b842f4e0a64afb952cef54909e6d8e
569,167,697,925,898,240
Camilleone
01/30/2022 04:34:47
maybe someone can draw and illustrate with a piecewise linear function and its derivative
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Ansh_
01/30/2022 04:35:06
Shuri ...:bearlain:
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Camilleone
01/30/2022 04:35:08
i'm out of paper space
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Ansh_
01/30/2022 04:35:46
Camilleone?
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Camilleone
01/30/2022 04:35:48
i use three colours to use the same paper three times, but i doubt it'll be clear in any sense of the word to anyone
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Camilleone
01/30/2022 04:36:50
yeah, you can use this, it's effectively the same argument but imo viewed from a slightly different angle
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Camilleone
01/30/2022 04:36:55
it ends up the same anyhow
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s_chanch
01/30/2022 04:37:12
wdym
1
0
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s_chanch
01/30/2022 04:37:27
so after adding these all up, what should you get..?
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Ansh_
01/30/2022 04:38:06
nothing >_< lmaooo, abs added something later
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s_chanch
01/30/2022 04:39:15
by ftc2, it should be f(b) - f(a), right..?
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Camilleone
01/30/2022 04:39:27
you're adding up the _infinitesimal_ increments at each point, and you get f(b) - f(a), or the increase of f from a to b
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s_chanch
01/30/2022 04:39:42
the expression of adding these up is integral of f’(x) from a to b
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s_chanch
01/30/2022 04:39:49
why
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s_chanch
01/30/2022 04:39:55
i don’t see how that’s intuitive
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Camilleone
01/30/2022 04:40:05
that's perfectly intuitive
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s_chanch
01/30/2022 04:40:09
not to me lol
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Camilleone
01/30/2022 04:40:09
take a rectangle
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Camilleone
01/30/2022 04:40:26
height c from 0 to 1
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help-10
d8b842f4e0a64afb952cef54909e6d8e
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abs_0
01/30/2022 04:40:36
Oops sorry yeah that was a bad explanation
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Camilleone
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Camilleone
01/30/2022 04:40:40
(you can replace 0 and 1 with arbitrary values but not the point)
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d8b842f4e0a64afb952cef54909e6d8e
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Camilleone
01/30/2022 04:41:48
do you agree that this rectangle, which is really a function y = c from 0 to 1, makes its antiderivative increase by c between 0 and 1?
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s_chanch
01/30/2022 04:43:00
not really
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s_chanch
01/30/2022 04:43:14
makes sense but only after evaluation
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s_chanch
01/30/2022 04:43:22
not intuition
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abs_0
01/30/2022 04:44:15
Good way of putting it
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Camilleone
01/30/2022 04:44:21
and this is where acceleration and velocity makes it dead useful to understand intuitively, and we're back to physics intuition
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abs_0
01/30/2022 04:44:28
Lol
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Camilleone
01/30/2022 04:45:26
you accelerate at rate c for all of one second, which means you end up with an increase of velocity by c at the end of that one second
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Camilleone
01/30/2022 04:45:35
but okay, since you hate physics
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Camilleone
01/30/2022 04:45:52
and sometimes after my physics class i can't blame you for it
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Camilleone
01/30/2022 04:46:56
the idea is that the antiderivative changes at a constant rate of c per unit over one unit, and so over that same one unit must increase by a value of c
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s_chanch
01/30/2022 04:54:01
wdym
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Camilleone
01/30/2022 05:04:05
the rate of change is c per unit
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help-10
d8b842f4e0a64afb952cef54909e6d8e
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Camilleone
01/30/2022 05:04:13
it literally means over one unit, the increment is c
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Camilleone
01/30/2022 05:04:17
this is by definition
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s_chanch
01/30/2022 05:09:30
(i’ll come back later)
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yue
01/30/2022 05:29:16
how would i take the laplace G(s) of this thing?
https://cdn.discordapp.c…7360/unknown.png
unknown.png
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Ansh_
01/30/2022 05:39:50
You mean, it's Laplace transform?
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yue
01/30/2022 05:40:30
yes
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Ansh_
01/30/2022 05:47:15
Let $f(t) = t \sin(40t)$, then by IBP, you'll have \\ $\mathcal{L}\{g(t)\} = \mathcal{L}\{f"(t)\} = s^2\mathcal{L}\{f(t)\} - sf(0) -f'(0)$
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TeXit
01/30/2022 05:47:28
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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a4df4381742f40f7add426a3c996ade1
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Ansh_
01/30/2022 05:48:16
https://math.libretexts.org/Bookshelves/Differential_Equations/Book%3A_Differential_Equations_for_Engineers_(Lebl)/6%3A_The_Laplace_Transform/6.2%3A_Transforms_of_derivatives_and_ODEs
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Ansh_
01/30/2022 05:48:20
:this:
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RepliedPencil
01/30/2022 05:48:31
Yes ^^
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Ansh_
01/30/2022 05:48:39
You could also totally differentiate it twice, and then do the transform
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RepliedPencil
01/30/2022 05:48:51
It would be a lot complicated tho
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Ansh_
01/30/2022 05:48:58
Exactly
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Herels
01/30/2022 05:48:59
pain
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RepliedPencil
01/30/2022 05:50:14
Like you get g(t) as 40(sin(40t) - 40cos(40t)) And doing Laplace Transform of this is.... Just no
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Ansh_
01/30/2022 05:57:00
kek
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CherokeesMum
01/30/2022 05:59:00
Hello!
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CherokeesMum
01/30/2022 05:59:11
Would anyone happen to have a clue if I did this question correctly?
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CherokeesMum
01/30/2022 05:59:12
https://cdn.discordapp.c…1071/unknown.png
unknown.png
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CherokeesMum
01/30/2022 05:59:41
https://cdn.discordapp.c…560/IMG_3111.jpg
IMG_3111.jpg
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CherokeesMum
01/30/2022 06:00:01
https://cdn.discordapp.c…0754/unknown.png
unknown.png
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CherokeesMum
01/30/2022 06:00:47
I just don't know if for part b, I used the right n. Like if n should be 4 because I used the first four terms of the series
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Sparky
01/30/2022 06:17:18
if this is your result for a it is not correct. you need to a partial fracture disassembly i guess.
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CherokeesMum
01/30/2022 06:27:14
Oh okay
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CherokeesMum
01/30/2022 06:27:36
I've never heard of a partial fracture disassembly before
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Ansh_
01/30/2022 07:07:06
:p A partial fracture disassembly, although probably not even a proper English term, should be referring to disassembling of a bone that's partially been fractured( the crack hasn't reached across the width of the bone ), maybe for some medical purposes, like reassembling when misconfigured... or stuff Anyways
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Ansh_
01/30/2022 07:07:38
For your question, if you're interested in R4, you should stick to the formula and plug n = 4, to both sides of the inequality
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CherokeesMum
01/30/2022 07:08:19
Hiiiiiii
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CherokeesMum
01/30/2022 07:08:23
Thank you for helping
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Ansh_
01/30/2022 07:08:33
So your inequality would look like $|R_4| < \qty|\frac{(-1)^{5+1}}{4(5)^2 -3}|$
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TeXit
01/30/2022 07:08:35
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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CherokeesMum
01/30/2022 07:08:35
I’m not sure if it’s n=4 or 5 that I should use
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6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:08:47
Oh
1
0
null
null
null
null
null
367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:08:53
I did the RHS wrong
1
0
null
null
null
null
null
367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:09:57
Thank you, that was very helpful
1
0
null
null
null
null
null
367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:10:06
Though what do you think of part a?
1
0
null
null
null
null
null
367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:10:16
Sparky said it was incorrect earlier
1
0
null
null
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null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:10:21
I thought it was okay
1
0
null
null
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null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:10:38
Don’t you just find each of the four terms individually then add them up?
1
0
null
null
null
null
null
367
help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:13:56
https://youtu.be/H8lHvQashkE
0
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:14:04
:this: watch once and you'll know
0
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
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CherokeesMum
01/30/2022 07:18:12
Yup
1
0
null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:18:14
Thank you
1
0
null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:18:29
I can see that the method I was doing was wrong
1
0
null
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null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:18:34
mmm
0
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:18:35
Wow that really opened my eyes
1
0
819,940,147,013,222,400
CherokeesMum
6349
CherokeesMum
false
367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:18:48
I wish that was stated clearer in my lecture notes
1
0
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help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:19:05
I'm going to see if it said it any where
1
0
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:21:55
This is the closest I could get
1
0
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help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:21:57
https://cdn.discordapp.c…3354/unknown.png
unknown.png
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:25:34
:catThink:
0
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help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:27:31
She also just added them, up to 6 terms, no?
0
1
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null
null
null
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367
help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:28:04
Like .1 - .04 + .009 - .0016 + .00025 - .000036 is what she did in the video
0
1
null
null
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help-10
6692c4aeb81d402fa444aba3e1294e81
706,934,233,012,371,600
Ansh_
01/30/2022 07:29:19
there's nothing wrong with your first part.. and logically, since the sum is convergent, and as n increases, each successive S_n value should be converging to the limiting value, S_4 is indeed what you want tbh
0
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
701,895,792,763,600,900
s_chanch
01/30/2022 07:29:20
(ansh, could you verify my statement in math discussion after helping janet?)
0
1
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help-10
6692c4aeb81d402fa444aba3e1294e81
819,940,147,013,222,400
CherokeesMum
01/30/2022 07:31:12
Okay so what I did was okay?
1
0
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null
null
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null